 P.P.3.1: In Exercises 1 to 10, match the descriptions, labeled A to  1 J, w...
 P.P.6.1: In Exercises 1 to 10, write the complex number in standard form. 181
 P.1: Evaluate 2x 8 3  4(3xy  z 2 ) for x = 2, y = 3, and z = 4
 P.P.4.1: In Exercises 1 to 8, factor out the GCF from each polynomial. 5x + 20
 P.P.2.1: In Exercises 1 to 12, evaluate each expression. 53
 P.P.5.1: In Exercises 1 to 10, simplify each rational expression. x2  x  2...
 P.P.1.1: In Exercises 1 and 2, determine whether each number is an integer, ...
 P.P.3.2: In Exercises 1 to 10, match the descriptions, labeled A to  1 J, w...
 P.P.6.2: In Exercises 1 to 10, write the complex number in standard form. 164
 P.2: Simplify: 5  2[3x  5(2x  3) + 1]
 P.P.4.2: In Exercises 1 to 8, factor out the GCF from each polynomial. 8x2 +...
 P.P.2.2: In Exercises 1 to 12, evaluate each expression. (5)3
 P.P.5.2: In Exercises 1 to 10, simplify each rational expression. 2x2  5x ...
 P.P.1.2: In Exercises 1 and 2, determine whether each number is an integer, ...
 P.P.3.3: In Exercises 1 to 10, match the descriptions, labeled A to  1 J, w...
 P.P.6.3: In Exercises 1 to 10, write the complex number in standard form. 198
 P.3: Simplify: 24x3 y4 6x2 y
 P.P.4.3: In Exercises 1 to 8, factor out the GCF from each polynomial. 15x2...
 P.P.2.3: In Exercises 1 to 12, evaluate each expression. a23b0
 P.P.5.3: In Exercises 1 to 10, simplify each rational expression. x3  9xx3 ...
 P.P.1.3: In Exercises 3 to 8, list the four smallest elements of each set. 5...
 P.P.3.4: In Exercises 1 to 10, match the descriptions, labeled A to  1 J, w...
 P.P.6.4: In Exercises 1 to 10, write the complex number in standard form. 127
 P.4: Simplify: (3a1>2 b3>4 ) 2 (2a2>3 b5>6 ) 3
 P.P.4.4: In Exercises 1 to 8, factor out the GCF from each polynomial. 6y2 ...
 P.P.2.4: In Exercises 1 to 12, evaluate each expression. 60
 P.P.5.4: In Exercises 1 to 10, simplify each rational expression. x3 + 1252x...
 P.P.1.4: In Exercises 3 to 8, list the four smallest elements of each set. x...
 P.P.3.5: In Exercises 1 to 10, match the descriptions, labeled A to  1 J, w...
 P.P.6.5: In Exercises 1 to 10, write the complex number in standard form. 11...
 P.5: Simplify: 23 16a4 b9 c8
 P.P.4.5: In Exercises 1 to 8, factor out the GCF from each polynomial. 10x2y...
 P.P.2.5: In Exercises 1 to 12, evaluate each expression. 42
 P.P.5.5: In Exercises 1 to 10, simplify each rational expression. a3 + 8a2  4
 P.P.1.5: In Exercises 3 to 8, list the four smallest elements of each set. 5...
 P.P.3.6: In Exercises 1 to 10, match the descriptions, labeled A to  1 J, w...
 P.P.6.6: In Exercises 1 to 10, write the complex number in standard form. 12...
 P.6: Simplify: 2 3  215
 P.P.4.6: In Exercises 1 to 8, factor out the GCF from each polynomial. 6a3b2...
 P.P.2.6: In Exercises 1 to 12, evaluate each expression. 34
 P.P.5.6: In Exercises 1 to 10, simplify each rational expression. y3  27y2...
 P.P.1.6: In Exercises 3 to 8, list the four smallest elements of each set. 5...
 P.P.3.7: In Exercises 1 to 10, match the descriptions, labeled A to  1 J, w...
 P.P.6.7: In Exercises 1 to 10, write the complex number in standard form. 5 ...
 P.7: Multiply: (3x  4y)(2x + 5y)
 P.P.4.7: In Exercises 1 to 8, factor out the GCF from each polynomial. (x  ...
 P.P.2.7: In Exercises 1 to 12, evaluate each expression. 125
 P.P.5.7: In Exercises 1 to 10, simplify each rational expression. x2 + 3x  ...
 P.P.1.7: In Exercises 3 to 8, list the four smallest elements of each set. 5...
 P.P.3.8: In Exercises 1 to 10, match the descriptions, labeled A to  1 J, w...
 P.P.6.8: In Exercises 1 to 10, write the complex number in standard form. 6 ...
 P.8: Multiply: (2a + 7)2
 P.P.4.8: In Exercises 1 to 8, factor out the GCF from each polynomial. (x  ...
 P.P.2.8: In Exercises 1 to 12, evaluate each expression. 133
 P.P.5.8: In Exercises 1 to 10, simplify each rational expression. 2x3  6x2 ...
 P.P.1.8: In Exercises 3 to 8, list the four smallest elements of each set. 5...
 P.P.3.9: In Exercises 1 to 10, match the descriptions, labeled A to  1 J, w...
 P.P.6.9: In Exercises 1 to 10, write the complex number in standard form. 8 ...
 P.9: Multiply: (2x  3)(4x2 5x  7)
 P.P.4.9: In Exercises 9 to 22, factor each trinomial over the integers. x2 +...
 P.P.2.9: In Exercises 1 to 12, evaluate each expression. 2363
 P.P.5.9: In Exercises 1 to 10, simplify each rational expression. 4y3  8y2 ...
 P.P.1.9: In Exercises 9 to 18, perform the operations given that A {3, 2, 1,...
 P.P.3.10: In Exercises 1 to 10, match the descriptions, labeled A to  1 J, w...
 P.P.6.10: In Exercises 1 to 10, write the complex number in standard form. 11...
 P.10: In Exercises 9 and 10, graph each interval and write the interval i...
 P.P.4.10: In Exercises 9 to 22, factor each trinomial over the integers. x2 +...
 P.P.2.10: In Exercises 1 to 12, evaluate each expression. 4223
 P.P.5.10: In Exercises 1 to 10, simplify each rational expression. x3  x2 + ...
 P.P.1.10: In Exercises 9 to 18, perform the operations given that A {3, 2, 1,...
 P.P.1.11: In Exercises 9 to 18, perform the operations given that A {3, 2, 1,...
 P.P.3.11: In Exercises 11 to 16, for each polynomial, determine its a. standa...
 P.P.6.11: In Exercises 11 to 36, simplify and write the complex number in sta...
 P.11: In Exercises 11 and 12, graph each set and write the set in interva...
 P.P.4.11: In Exercises 9 to 22, factor each trinomial over the integers. a2 ...
 P.P.2.11: In Exercises 1 to 12, evaluate each expression. 2x0
 P.P.5.11: In Exercises 11 to 40, simplify each expression. a 4a3b2 b a 6ba4 b
 P.P.1.12: In Exercises 9 to 18, perform the operations given that A {3, 2, 1,...
 P.P.3.12: In Exercises 11 to 16, for each polynomial, determine its a. standa...
 P.P.6.12: In Exercises 11 to 36, simplify and write the complex number in sta...
 P.12: In Exercises 11 and 12, graph each set and write the set in interva...
 P.P.4.12: In Exercises 9 to 22, factor each trinomial over the integers. b2 +...
 P.P.2.12: In Exercises 1 to 12, evaluate each expression. x04
 P.P.5.12: In Exercises 11 to 40, simplify each expression. a12x2y5z4 b a 25x...
 P.P.1.13: In Exercises 9 to 18, perform the operations given that A {3, 2, 1,...
 P.P.3.13: In Exercises 11 to 16, for each polynomial, determine its a. standa...
 P.P.6.13: In Exercises 11 to 36, simplify and write the complex number in sta...
 P.13: In Exercises 13 to 18, write each expression without absolute value...
 P.P.4.13: In Exercises 9 to 22, factor each trinomial over the integers. x2 +...
 P.P.2.13: In Exercises 13 to 38, write the exponential expression in simplest...
 P.P.5.13: In Exercises 11 to 40, simplify each expression. a6p25q2 b1a 2p3q2 b2
 P.P.1.14: In Exercises 9 to 18, perform the operations given that A {3, 2, 1,...
 P.P.3.14: In Exercises 11 to 16, for each polynomial, determine its a. standa...
 P.P.6.14: In Exercises 11 to 36, simplify and write the complex number in sta...
 P.14: In Exercises 13 to 18, write each expression without absolute value...
 P.P.4.14: In Exercises 9 to 22, factor each trinomial over the integers. x2 +...
 P.P.2.14: In Exercises 13 to 38, write the exponential expression in simplest...
 P.P.5.14: In Exercises 11 to 40, simplify each expression. a4r2s3t3 b1a6rs35...
 P.P.1.15: In Exercises 9 to 18, perform the operations given that A {3, 2, 1,...
 P.P.3.15: In Exercises 11 to 16, for each polynomial, determine its a. standa...
 P.P.6.15: In Exercises 11 to 36, simplify and write the complex number in sta...
 P.15: In Exercises 13 to 18, write each expression without absolute value...
 P.P.4.15: In Exercises 9 to 22, factor each trinomial over the integers. 6x2 ...
 P.P.2.15: In Exercises 13 to 38, write the exponential expression in simplest...
 P.P.5.15: In Exercises 11 to 40, simplify each expression. x2 + x2x + 3# 3x2 ...
 P.P.1.16: In Exercises 9 to 18, perform the operations given that A {3, 2, 1,...
 P.P.3.16: In Exercises 11 to 16, for each polynomial, determine its a. standa...
 P.P.6.16: In Exercises 11 to 36, simplify and write the complex number in sta...
 P.16: In Exercises 13 to 18, write each expression without absolute value...
 P.P.4.16: In Exercises 9 to 22, factor each trinomial over the integers. 8a2 ...
 P.P.2.16: In Exercises 13 to 38, write the exponential expression in simplest...
 P.P.5.16: In Exercises 11 to 40, simplify each expression. x2  16x2 + 7x + 1...
 P.P.1.17: In Exercises 9 to 18, perform the operations given that A {3, 2, 1,...
 P.P.3.17: In Exercises 17 to 22, determine the degree of the given polynomial...
 P.P.6.17: In Exercises 11 to 36, simplify and write the complex number in sta...
 P.17: In Exercises 13 to 18, write each expression without absolute value...
 P.P.4.17: In Exercises 9 to 22, factor each trinomial over the integers. 51x2...
 P.P.2.17: In Exercises 13 to 38, write the exponential expression in simplest...
 P.P.5.17: In Exercises 11 to 40, simplify each expression. 3x  152x2  50# 2...
 P.P.1.18: In Exercises 9 to 18, perform the operations given that A {3, 2, 1,...
 P.P.3.18: In Exercises 17 to 22, determine the degree of the given polynomial...
 P.P.6.18: In Exercises 11 to 36, simplify and write the complex number in sta...
 P.18: In Exercises 13 to 18, write each expression without absolute value...
 P.P.4.18: In Exercises 9 to 22, factor each trinomial over the integers. 57y2...
 P.P.2.18: In Exercises 13 to 38, write the exponential expression in simplest...
 P.P.5.18: In Exercises 11 to 40, simplify each expression. y3  8y2 + y  6# ...
 P.P.1.19: In Exercises 19 to 24, perform the operation, given A is any set. A A
 P.P.3.19: In Exercises 17 to 22, determine the degree of the given polynomial...
 P.P.6.19: In Exercises 11 to 36, simplify and write the complex number in sta...
 P.19: If 3 and 7 are the coordinates of two points on the real number li...
 P.P.4.19: In Exercises 9 to 22, factor each trinomial over the integers. 6x2 ...
 P.P.2.19: In Exercises 13 to 38, write the exponential expression in simplest...
 P.P.5.19: In Exercises 11 to 40, simplify each expression. 12y2 + 28y + 156y2...
 P.P.1.20: In Exercises 19 to 24, perform the operation, given A is any set. A A
 P.P.3.20: In Exercises 17 to 22, determine the degree of the given polynomial...
 P.P.6.20: In Exercises 11 to 36, simplify and write the complex number in sta...
 P.20: If a = 4 and b = 1 are the coordinates of two points on the real n...
 P.P.4.20: In Exercises 9 to 22, factor each trinomial over the integers. 8x2 ...
 P.P.2.20: In Exercises 13 to 38, write the exponential expression in simplest...
 P.P.5.20: In Exercises 11 to 40, simplify each expression. z2  81z2  16 , z...
 P.P.1.21: In Exercises 19 to 24, perform the operation, given A is any set. A
 P.P.3.21: In Exercises 17 to 22, determine the degree of the given polynomial.xy
 P.P.6.21: In Exercises 11 to 36, simplify and write the complex number in sta...
 P.21: In Exercises 21 to 24, evaluate the expression. 44
 P.P.4.21: In Exercises 9 to 22, factor each trinomial over the integers. 6x2 ...
 P.P.2.21: In Exercises 13 to 38, write the exponential expression in simplest...
 P.P.5.21: In Exercises 11 to 40, simplify each expression. a2 + 9a2  64 , a3...
 P.P.1.22: In Exercises 19 to 24, perform the operation, given A is any set. A
 P.P.3.22: In Exercises 17 to 22, determine the degree of the given polynomial...
 P.P.6.22: In Exercises 11 to 36, simplify and write the complex number in sta...
 P.22: In Exercises 21 to 24, evaluate the expression. 42 (3)2
 P.P.4.22: In Exercises 9 to 22, factor each trinomial over the integers. 9x2 ...
 P.P.2.22: In Exercises 13 to 38, write the exponential expression in simplest...
 P.P.5.22: In Exercises 11 to 40, simplify each expression. 6x2 + 13xy + 6y24x...
 P.P.1.23: In Exercises 19 to 24, perform the operation, given A is any set. I...
 P.P.3.23: In Exercises 23 to 40, perform the indicated operation and simplify...
 P.P.6.23: In Exercises 11 to 36, simplify and write the complex number in sta...
 P.23: In Exercises 21 to 24, evaluate the expression. 5 # 32 + 455  23...
 P.P.4.23: In Exercises 23 to 28, use the factorization theorem to determine w...
 P.P.2.23: In Exercises 13 to 38, write the exponential expression in simplest...
 P.P.5.23: In Exercises 11 to 40, simplify each expression. p + 5r +2p  7r
 P.P.1.24: In Exercises 19 to 24, perform the operation, given A is any set. I...
 P.P.3.24: In Exercises 23 to 40, perform the indicated operation and simplify...
 P.P.6.24: In Exercises 11 to 36, simplify and write the complex number in sta...
 P.24: In Exercises 21 to 24, evaluate the expression. 6  2c4  (5)2  2...
 P.P.4.24: In Exercises 23 to 28, use the factorization theorem to determine w...
 P.P.2.24: In Exercises 13 to 38, write the exponential expression in simplest...
 P.P.5.24: In Exercises 11 to 40, simplify each expression. 2s + 5t4t+ 2s + 3t4t
 P.P.1.25: In Exercises 25 to 36, graph each set. Write sets given in interval...
 P.P.3.25: In Exercises 23 to 40, perform the indicated operation and simplify...
 P.P.6.25: In Exercises 11 to 36, simplify and write the complex number in sta...
 P.25: In Exercises 25 and 26, evaluate the variable expressions for x 2, ...
 P.P.4.25: In Exercises 23 to 28, use the factorization theorem to determine w...
 P.P.2.25: In Exercises 13 to 38, write the exponential expression in simplest...
 P.P.5.25: In Exercises 11 to 40, simplify each expression. 5y  7y + 4  2y ...
 P.P.1.26: In Exercises 25 to 36, graph each set. Write sets given in interval...
 P.P.3.26: In Exercises 23 to 40, perform the indicated operation and simplify...
 P.P.6.26: In Exercises 11 to 36, simplify and write the complex number in sta...
 P.26: In Exercises 25 and 26, evaluate the variable expressions for x 2, ...
 P.P.4.26: In Exercises 23 to 28, use the factorization theorem to determine w...
 P.P.2.26: In Exercises 13 to 38, write the exponential expression in simplest...
 P.P.5.26: In Exercises 11 to 40, simplify each expression. 6x  5x  3  3x ...
 P.P.1.27: In Exercises 25 to 36, graph each set. Write sets given in interval...
 P.P.3.27: In Exercises 23 to 40, perform the indicated operation and simplify...
 P.P.6.27: In Exercises 11 to 36, simplify and write the complex number in sta...
 P.27: In Exercises 27 to 34, identify the real number property or propert...
 P.P.4.27: In Exercises 23 to 28, use the factorization theorem to determine w...
 P.P.2.27: In Exercises 13 to 38, write the exponential expression in simplest...
 P.P.5.27: In Exercises 11 to 40, simplify each expression. xx  5+7xx + 3
 P.P.1.28: In Exercises 25 to 36, graph each set. Write sets given in interval...
 P.P.3.28: In Exercises 23 to 40, perform the indicated operation and simplify...
 P.P.6.28: In Exercises 11 to 36, simplify and write the complex number in sta...
 P.28: In Exercises 27 to 34, identify the real number property or propert...
 P.P.4.28: In Exercises 23 to 28, use the factorization theorem to determine w...
 P.P.2.28: In Exercises 13 to 38, write the exponential expression in simplest...
 P.P.5.28: In Exercises 11 to 40, simplify each expression. 2x3x + 1+5xx  7
 P.P.1.29: In Exercises 25 to 36, graph each set. Write sets given in interval...
 P.P.3.29: In Exercises 23 to 40, perform the indicated operation and simplify...
 P.P.6.29: In Exercises 11 to 36, simplify and write the complex number in sta...
 P.29: In Exercises 27 to 34, identify the real number property or propert...
 P.P.4.29: In Exercises 29 to 42, factor each difference of squares over the i...
 P.P.2.29: In Exercises 13 to 38, write the exponential expression in simplest...
 P.P.5.29: In Exercises 11 to 40, simplify each expression. 4z2z  3+5zz  5
 P.P.1.30: In Exercises 25 to 36, graph each set. Write sets given in interval...
 P.P.3.30: In Exercises 23 to 40, perform the indicated operation and simplify...
 P.P.6.30: In Exercises 11 to 36, simplify and write the complex number in sta...
 P.30: In Exercises 27 to 34, identify the real number property or propert...
 P.P.4.30: In Exercises 29 to 42, factor each difference of squares over the i...
 P.P.2.30: In Exercises 13 to 38, write the exponential expression in simplest...
 P.P.5.30: In Exercises 11 to 40, simplify each expression. 3y  13y + 1  2y ...
 P.P.1.31: In Exercises 25 to 36, graph each set. Write sets given in interval...
 P.P.3.31: In Exercises 23 to 40, perform the indicated operation and simplify...
 P.P.6.31: In Exercises 11 to 36, simplify and write the complex number in sta...
 P.31: In Exercises 27 to 34, identify the real number property or propert...
 P.P.4.31: In Exercises 29 to 42, factor each difference of squares over the i...
 P.P.2.31: In Exercises 13 to 38, write the exponential expression in simplest...
 P.P.5.31: In Exercises 11 to 40, simplify each expression. xx2  9  3x  1x2...
 P.P.1.32: In Exercises 25 to 36, graph each set. Write sets given in interval...
 P.P.3.32: In Exercises 23 to 40, perform the indicated operation and simplify...
 P.P.6.32: In Exercises 11 to 36, simplify and write the complex number in sta...
 P.32: In Exercises 27 to 34, identify the real number property or propert...
 P.P.4.32: In Exercises 29 to 42, factor each difference of squares over the i...
 P.P.2.32: In Exercises 13 to 38, write the exponential expression in simplest...
 P.P.5.32: In Exercises 11 to 40, simplify each expression. m  nm2  mn  6n2...
 P.P.1.33: In Exercises 25 to 36, graph each set. Write sets given in interval...
 P.P.3.33: In Exercises 23 to 40, perform the indicated operation and simplify...
 P.P.6.33: In Exercises 11 to 36, simplify and write the complex number in sta...
 P.33: In Exercises 27 to 34, identify the real number property or propert...
 P.P.4.33: In Exercises 29 to 42, factor each difference of squares over the i...
 P.P.2.33: In Exercises 13 to 38, write the exponential expression in simplest...
 P.P.5.33: In Exercises 11 to 40, simplify each expression. 1x +23x  1# 3x2 +...
 P.P.1.34: In Exercises 25 to 36, graph each set. Write sets given in interval...
 P.P.3.34: In Exercises 23 to 40, perform the indicated operation and simplify...
 P.P.6.34: In Exercises 11 to 36, simplify and write the complex number in sta...
 P.34: In Exercises 27 to 34, identify the real number property or propert...
 P.P.4.34: In Exercises 29 to 42, factor each difference of squares over the i...
 P.P.2.34: In Exercises 13 to 38, write the exponential expression in simplest...
 P.P.5.34: In Exercises 11 to 40, simplify each expression. 2y  3y + 1#y2  1...
 P.P.1.35: In Exercises 25 to 36, graph each set. Write sets given in interval...
 P.P.3.35: In Exercises 23 to 40, perform the indicated operation and simplify...
 P.P.6.35: In Exercises 11 to 36, simplify and write the complex number in sta...
 P.35: In Exercises 35 and 36, simplify the variable expression. 8  3(2x ...
 P.P.4.35: In Exercises 29 to 42, factor each difference of squares over the i...
 P.P.2.35: In Exercises 13 to 38, write the exponential expression in simplest...
 P.P.5.35: In Exercises 11 to 40, simplify each expression. + 1q  3  2qq  3...
 P.P.1.36: In Exercises 25 to 36, graph each set. Write sets given in interval...
 P.P.3.36: In Exercises 23 to 40, perform the indicated operation and simplify...
 P.P.6.36: In Exercises 11 to 36, simplify and write the complex number in sta...
 P.36: In Exercises 35 and 36, simplify the variable expression. 5x  3[7 ...
 P.P.4.36: In Exercises 29 to 42, factor each difference of squares over the i...
 P.P.2.36: In Exercises 13 to 38, write the exponential expression in simplest...
 P.P.5.36: In Exercises 11 to 40, simplify each expression. pp + 5+ pp  4 , p...
 P.P.1.37: In Exercises 37 to 52, graph each set. ( q, 0) 32, 44
 P.P.3.37: In Exercises 23 to 40, perform the indicated operation and simplify...
 P.P.6.37: In Exercises 37 to 54, write each expression as a complex number in...
 P.37: In Exercises 37 to 40, simplify the exponential expression. 25
 P.P.4.37: In Exercises 29 to 42, factor each difference of squares over the i...
 P.P.2.37: In Exercises 13 to 38, write the exponential expression in simplest...
 P.P.5.37: In Exercises 11 to 40, simplify each expression. 1x2 + 7x + 12+1x2 ...
 P.P.1.38: In Exercises 37 to 52, graph each set. (3, 1) (3, 5)
 P.P.3.38: In Exercises 23 to 40, perform the indicated operation and simplify...
 P.P.6.38: In Exercises 37 to 54, write each expression as a complex number in...
 P.38: In Exercises 37 to 40, simplify the exponential expression.  1p0
 P.P.4.38: In Exercises 29 to 42, factor each difference of squares over the i...
 P.P.2.38: In Exercises 13 to 38, write the exponential expression in simplest...
 P.P.5.38: In Exercises 11 to 40, simplify each expression. 2a2  3a + 2+3a2 ...
 P.P.1.39: In Exercises 37 to 52, graph each set. (4, 0) 32, 54
 P.P.3.39: In Exercises 23 to 40, perform the indicated operation and simplify...
 P.P.6.39: In Exercises 37 to 54, write each expression as a complex number in...
 P.39: In Exercises 37 to 40, simplify the exponential expression. 2z4
 P.P.4.39: In Exercises 29 to 42, factor each difference of squares over the i...
 P.P.2.39: In Exercises 39 to 42, write the number in scientific notation. 2,0...
 P.P.5.39: In Exercises 11 to 40, simplify each expression. a1 +2xb a3  1xb
 P.P.1.40: In Exercises 37 to 52, graph each set. ( q, 34 (2, 6)
 P.P.3.40: In Exercises 23 to 40, perform the indicated operation and simplify...
 P.P.6.40: In Exercises 37 to 54, write each expression as a complex number in...
 P.40: In Exercises 37 to 40, simplify the exponential expression. x4y3
 P.P.4.40: In Exercises 29 to 42, factor each difference of squares over the i...
 P.P.2.40: In Exercises 39 to 42, write the number in scientific notation. 49,...
 P.P.5.40: In Exercises 11 to 40, simplify each expression. a4  1zb a4 +2zb
 P.P.1.41: In Exercises 37 to 52, graph each set. (1, q) (2, q)
 P.P.3.41: In Exercises 41 to 54, use the FOIL method to find the indicated pr...
 P.P.6.41: In Exercises 37 to 54, write each expression as a complex number in...
 P.41: In Exercises 41 and 42, write each number in scientific notation. 6...
 P.P.4.41: In Exercises 29 to 42, factor each difference of squares over the i...
 P.P.2.41: In Exercises 39 to 42, write the number in scientific notation. 0.0...
 P.P.5.41: In Exercises 41 to 58, simplify each complex fraction. 4 +1x1  1x
 P.P.1.42: In Exercises 37 to 52, graph each set. (4, q) (0, q)
 P.P.3.42: In Exercises 41 to 54, use the FOIL method to find the indicated pr...
 P.P.6.42: In Exercises 37 to 54, write each expression as a complex number in...
 P.42: In Exercises 41 and 42, write each number in scientific notation. 0...
 P.P.4.42: In Exercises 29 to 42, factor each difference of squares over the i...
 P.P.2.42: In Exercises 39 to 42, write the number in scientific notation. 0.0...
 P.P.5.42: In Exercises 41 to 58, simplify each complex fraction. 3  2a5 +3a
 P.P.1.43: In Exercises 37 to 52, graph each set. (1, q) (2, q)
 P.P.3.43: In Exercises 41 to 54, use the FOIL method to find the indicated pr...
 P.P.6.43: In Exercises 37 to 54, write each expression as a complex number in...
 P.43: In Exercises 43 and 44, change each number from scientific notation...
 P.P.4.43: In Exercises 43 to 50, factor each perfectsquare trinomial. x2 + 1...
 P.P.2.43: In Exercises 43 to 46, change the number from scientific notation t...
 P.P.5.43: In Exercises 41 to 58, simplify each complex fraction. xy  2y  x
 P.P.1.44: In Exercises 37 to 52, graph each set. (4, q) (0, q)
 P.P.3.44: In Exercises 41 to 54, use the FOIL method to find the indicated pr...
 P.P.6.44: In Exercises 37 to 54, write each expression as a complex number in...
 P.44: In Exercises 43 and 44, change each number from scientific notation...
 P.P.4.44: In Exercises 43 to 50, factor each perfectsquare trinomial. y2 + 6...
 P.P.2.44: In Exercises 43 to 46, change the number from scientific notation t...
 P.P.5.44: In Exercises 41 to 58, simplify each complex fraction. 3 +2x  34 +...
 P.P.1.45: In Exercises 37 to 52, graph each set. 32, 44 34, 54
 P.P.3.45: In Exercises 41 to 54, use the FOIL method to find the indicated pr...
 P.P.6.45: In Exercises 37 to 54, write each expression as a complex number in...
 P.45: In Exercises 45 to 48, evaluate each exponential expression. 251>2
 P.P.4.45: In Exercises 43 to 50, factor each perfectsquare trinomial.a2  14...
 P.P.2.45: In Exercises 43 to 46, change the number from scientific notation t...
 P.P.5.45: In Exercises 41 to 58, simplify each complex fraction. 5  1x + 21 ...
 P.P.1.46: In Exercises 37 to 52, graph each set. ( q, 14 31, q)
 P.P.3.46: In Exercises 41 to 54, use the FOIL method to find the indicated pr...
 P.P.6.46: In Exercises 37 to 54, write each expression as a complex number in...
 P.46: In Exercises 45 to 48, evaluate each exponential expression. 272>3
 P.P.4.46: In Exercises 43 to 50, factor each perfectsquare trinomial. b2  2...
 P.P.2.46: In Exercises 43 to 46, change the number from scientific notation t...
 P.P.5.46: In Exercises 41 to 58, simplify each complex fraction. 1(x + h)2  1h
 P.P.1.47: In Exercises 37 to 52, graph each set. (2, 4) (4, 5)
 P.P.3.47: In Exercises 41 to 54, use the FOIL method to find the indicated pr...
 P.P.6.47: In Exercises 37 to 54, write each expression as a complex number in...
 P.47: In Exercises 45 to 48, evaluate each exponential expression. 361>2
 P.P.4.47: In Exercises 43 to 50, factor each perfectsquare trinomial. 4x2 + ...
 P.P.2.47: In Exercises 47 to 54, perform the indicated operation and write th...
 P.P.5.47: In Exercises 41 to 58, simplify each complex fraction. 1 +1b  21 ...
 P.P.1.48: In Exercises 37 to 52, graph each set. ( q, 1) (1, q)
 P.P.3.48: In Exercises 41 to 54, use the FOIL method to find the indicated pr...
 P.P.6.48: In Exercises 37 to 54, write each expression as a complex number in...
 P.48: In Exercises 45 to 48, evaluate each exponential expression. 3811>4
 P.P.4.48: In Exercises 43 to 50, factor each perfectsquare trinomial. 25y2 +...
 P.P.2.48: In Exercises 47 to 54, perform the indicated operation and write th...
 P.P.5.48: In Exercises 41 to 58, simplify each complex fraction. r  rr +13
 P.P.1.49: In Exercises 37 to 52, graph each set. 5x x 6 36 5x 1 6 x 6 26
 P.P.3.49: In Exercises 41 to 54, use the FOIL method to find the indicated pr...
 P.P.6.49: In Exercises 37 to 54, write each expression as a complex number in...
 P.49: In Exercises 49 to 58, simplify the expression. (4x3y2)(6x4y3)
 P.P.4.49: In Exercises 43 to 50, factor each perfectsquare trinomial. z4 + 4...
 P.P.2.49: In Exercises 47 to 54, perform the indicated operation and write th...
 P.P.5.49: In Exercises 41 to 58, simplify each complex fraction. 1  1x21 +1x
 P.P.1.50: In Exercises 37 to 52, graph each set. 5x 3 x 6 06 5x x 26
 P.P.3.50: In Exercises 41 to 54, use the FOIL method to find the indicated pr...
 P.P.6.50: In Exercises 37 to 54, write each expression as a complex number in...
 P.50: In Exercises 49 to 58, simplify the expression. 12a5b18a3b6
 P.P.4.50: In Exercises 43 to 50, factor each perfectsquare trinomial. 9x4  ...
 P.P.2.50: In Exercises 47 to 54, perform the indicated operation and write th...
 P.P.5.50: In Exercises 41 to 58, simplify each complex fraction. 1a +1b
 P.P.1.51: In Exercises 37 to 52, graph each set. 5x x 6 36 5x x 6 26
 P.P.3.51: In Exercises 41 to 54, use the FOIL method to find the indicated pr...
 P.P.6.51: In Exercises 37 to 54, write each expression as a complex number in...
 P.51: In Exercises 49 to 58, simplify the expression. (3x2y3)3
 P.P.4.51: In Exercises 51 to 58, factor each sum or difference of cubes over ...
 P.P.2.51: In Exercises 47 to 54, perform the indicated operation and write th...
 P.P.5.51: In Exercises 41 to 58, simplify each complex fraction. 2  m1  1 ...
 P.P.1.52: In Exercises 37 to 52, graph each set. 5x x 6 36 5x x 6 26
 P.P.3.52: In Exercises 41 to 54, use the FOIL method to find the indicated pr...
 P.P.6.52: In Exercises 37 to 54, write each expression as a complex number in...
 P.52: In Exercises 49 to 58, simplify the expression. a2a2b46a3b6 b2
 P.P.4.52: In Exercises 51 to 58, factor each sum or difference of cubes over ...
 P.P.2.52: In Exercises 47 to 54, perform the indicated operation and write th...
 P.P.5.52: In Exercises 41 to 58, simplify each complex fraction. x + h + 1x +...
 P.P.1.53: In Exercises 53 to 62, write each expression without absolute value...
 P.P.3.53: In Exercises 41 to 54, use the FOIL method to find the indicated pr...
 P.P.6.53: In Exercises 37 to 54, write each expression as a complex number in...
 P.53: In Exercises 49 to 58, simplify the expression. (4x3y2)2(8x2y3)2
 P.P.4.53: In Exercises 51 to 58, factor each sum or difference of cubes over ...
 P.P.2.53: In Exercises 47 to 54, perform the indicated operation and write th...
 P.P.5.53: In Exercises 41 to 58, simplify each complex fraction. x  x  4x +...
 P.P.1.54: In Exercises 53 to 62, write each expression without absolute value...
 P.P.3.54: In Exercises 41 to 54, use the FOIL method to find the indicated pr...
 P.P.6.54: In Exercises 37 to 54, write each expression as a complex number in...
 P.54: In Exercises 49 to 58, simplify the expression. (2x4y5)3(4x3y4)2
 P.P.4.54: In Exercises 51 to 58, factor each sum or difference of cubes over ...
 P.P.2.54: In Exercises 47 to 54, perform the indicated operation and write th...
 P.P.5.54: In Exercises 41 to 58, simplify each complex fraction. 2y  3y  2y...
 P.P.1.55: In Exercises 53 to 62, write each expression without absolute value...
 P.P.3.55: In Exercises 55 to 62, use the special product formulas to perform ...
 P.P.6.55: In Exercises 55 to 62, evaluate the power of i. i15
 P.55: In Exercises 49 to 58, simplify the expression. (x1>2)(x3>4)
 P.P.4.55: In Exercises 51 to 58, factor each sum or difference of cubes over ...
 P.P.2.55: In Exercises 55 to 76, evaluate each exponential expression. 43>2
 P.P.5.55: In Exercises 41 to 58, simplify each complex fraction. x + 3  2x ...
 P.P.1.56: In Exercises 53 to 62, write each expression without absolute value...
 P.P.3.56: In Exercises 55 to 62, use the special product formulas to perform ...
 P.P.6.56: In Exercises 55 to 62, evaluate the power of i. i66
 P.56: In Exercises 49 to 58, simplify the expression. a2>3b3>4a5>6b2
 P.P.4.56: In Exercises 51 to 58, factor each sum or difference of cubes over ...
 P.P.2.56: In Exercises 55 to 76, evaluate each exponential expression. 163>2
 P.P.5.56: In Exercises 41 to 58, simplify each complex fraction. x + 2x2  1+...
 P.P.1.57: In Exercises 53 to 62, write each expression without absolute value...
 P.P.3.57: In Exercises 55 to 62, use the special product formulas to perform ...
 P.P.6.57: In Exercises 55 to 62, evaluate the power of i. i40
 P.57: In Exercises 49 to 58, simplify the expression. a8x5/4x1/2 b2>3
 P.P.4.57: In Exercises 51 to 58, factor each sum or difference of cubes over ...
 P.P.2.57: In Exercises 55 to 76, evaluate each exponential expression. 642>3
 P.P.5.57: In Exercises 41 to 58, simplify each complex fraction. x2 + 3x  10...
 P.P.1.58: In Exercises 53 to 62, write each expression without absolute value...
 P.P.3.58: In Exercises 55 to 62, use the special product formulas to perform ...
 P.P.6.58: In Exercises 55 to 62, evaluate the power of i. i51
 P.58: In Exercises 49 to 58, simplify the expression. a x2yx1/2y3 b1>2
 P.P.4.58: In Exercises 51 to 58, factor each sum or difference of cubes over ...
 P.P.2.58: In Exercises 55 to 76, evaluate each exponential expression. 1254>3
 P.P.5.58: In Exercises 41 to 58, simplify each complex fraction. 2y2 + 11y + ...
 P.P.1.59: In Exercises 53 to 62, write each expression without absolute value...
 P.P.3.59: In Exercises 55 to 62, use the special product formulas to perform ...
 P.P.6.59: In Exercises 55 to 62, evaluate the power of i. 1i25
 P.59: In Exercises 59 to 72, simplify each radical expression. Assume tha...
 P.P.4.59: In Exercises 59 to 66, factor over the integers the polynomials tha...
 P.P.2.59: In Exercises 55 to 76, evaluate each exponential expression. 93>2
 P.P.5.59: In Exercises 59 to 62, simplify each algebraic fraction. Write all ...
 P.P.1.60: In Exercises 53 to 62, write each expression without absolute value...
 P.P.3.60: In Exercises 55 to 62, use the special product formulas to perform ...
 P.P.6.60: In Exercises 55 to 62, evaluate the power of i. 1i83
 P.60: In Exercises 59 to 72, simplify each radical expression. Assume tha...
 P.P.4.60: In Exercises 59 to 66, factor over the integers the polynomials tha...
 P.P.2.60: In Exercises 55 to 76, evaluate each exponential expression. 324>5
 P.P.5.60: In Exercises 59 to 62, simplify each algebraic fraction. Write all ...
 P.P.1.61: In Exercises 53 to 62, write each expression without absolute value...
 P.P.3.61: In Exercises 55 to 62, use the special product formulas to perform ...
 P.P.6.61: In Exercises 55 to 62, evaluate the power of i. i 34
 P.61: In Exercises 59 to 72, simplify each radical expression. Assume tha...
 P.P.4.61: In Exercises 59 to 66, factor over the integers the polynomials tha...
 P.P.2.61: In Exercises 55 to 76, evaluate each exponential expression. a49b1>2
 P.P.5.61: In Exercises 59 to 62, simplify each algebraic fraction. Write all ...
 P.P.1.62: In Exercises 53 to 62, write each expression without absolute value...
 P.P.3.62: In Exercises 55 to 62, use the special product formulas to perform ...
 P.P.6.62: In Exercises 55 to 62, evaluate the power of i. i 52
 P.62: In Exercises 59 to 72, simplify each radical expression. Assume tha...
 P.P.4.62: In Exercises 59 to 66, factor over the integers the polynomials tha...
 P.P.2.62: In Exercises 55 to 76, evaluate each exponential expression. a1625 ...
 P.P.5.62: In Exercises 59 to 62, simplify each algebraic fraction. Write all ...
 P.P.5.63: Average Speed According to Example 8, the average speed for a round...
 P.P.1.63: In Exercises 63 to 74, use absolute value notation to describe the ...
 P.P.3.63: In Exercises 63 to 68, perform the indicated operation or operation...
 P.P.6.63: In Exercises 63 to 68, evaluate b 2b2 4ac 2ai for the given values ...
 P.63: In Exercises 59 to 72, simplify each radical expression. Assume tha...
 P.P.4.63: In Exercises 59 to 66, factor over the integers the polynomials tha...
 P.P.2.63: In Exercises 55 to 76, evaluate each exponential expression. a18b4>3
 P.P.5.64: Relativity Theory Using Einsteins Theory of Relativity, the sum of ...
 P.P.1.64: In Exercises 63 to 74, use absolute value notation to describe the ...
 P.P.3.64: In Exercises 63 to 68, perform the indicated operation or operation...
 P.P.6.64: In Exercises 63 to 68, evaluate b 2b2 4ac 2ai for the given values ...
 P.64: In Exercises 59 to 72, simplify each radical expression. Assume tha...
 P.P.4.64: In Exercises 59 to 66, factor over the integers the polynomials tha...
 P.P.2.64: In Exercises 55 to 76, evaluate each exponential expression. a 827 ...
 P.P.5.65: Find the rational expression in simplest form that represents the s...
 P.P.1.65: In Exercises 63 to 74, use absolute value notation to describe the ...
 P.P.3.65: In Exercises 63 to 68, perform the indicated operation or operation...
 P.P.6.65: In Exercises 63 to 68, evaluate b 2b2 4ac 2ai for the given values ...
 P.65: In Exercises 59 to 72, simplify each radical expression. Assume tha...
 P.P.4.65: In Exercises 59 to 66, factor over the integers the polynomials tha...
 P.P.2.65: In Exercises 55 to 76, evaluate each exponential expression. (4a 2>...
 P.P.5.66: Find the rational expression in simplest form that represents the p...
 P.P.1.66: In Exercises 63 to 74, use absolute value notation to describe the ...
 P.P.3.66: In Exercises 63 to 68, perform the indicated operation or operation...
 P.P.6.66: In Exercises 63 to 68, evaluate b 2b2 4ac 2ai for the given values ...
 P.66: In Exercises 59 to 72, simplify each radical expression. Assume tha...
 P.P.4.66: In Exercises 59 to 66, factor over the integers the polynomials tha...
 P.P.2.66: In Exercises 55 to 76, evaluate each exponential expression. (6a3>5...
 P.P.5.67: Find the rational expression in simplest form that represents the s...
 P.P.1.67: In Exercises 63 to 74, use absolute value notation to describe the ...
 P.P.3.67: In Exercises 63 to 68, perform the indicated operation or operation...
 P.P.6.67: In Exercises 63 to 68, evaluate b 2b2 4ac 2ai for the given values ...
 P.67: In Exercises 59 to 72, simplify each radical expression. Assume tha...
 P.P.4.67: In Exercises 67 to 72, factor over the integers by grouping. 3x3 + ...
 P.P.2.67: In Exercises 55 to 76, evaluate each exponential expression. (3x )...
 P.P.5.68: Find the rational expression in simplest form that represents the s...
 P.P.1.68: In Exercises 63 to 74, use absolute value notation to describe the ...
 P.P.3.68: In Exercises 63 to 68, perform the indicated operation or operation...
 P.P.6.68: In Exercises 63 to 68, evaluate b 2b2 4ac 2ai for the given values ...
 P.68: In Exercises 59 to 72, simplify each radical expression. Assume tha...
 P.P.4.68: In Exercises 67 to 72, factor over the integers by grouping. 18w3 +...
 P.P.2.68: In Exercises 55 to 76, evaluate each exponential expression. (5x1>...
 P.P.1.69: In Exercises 63 to 74, use absolute value notation to describe the ...
 P.P.3.69: In Exercises 69 to 76, evaluate the given polynomial for the indica...
 P.69: In Exercises 59 to 72, simplify each radical expression. Assume tha...
 P.P.4.69: In Exercises 67 to 72, factor over the integers by grouping. ax2  ...
 P.P.2.69: In Exercises 55 to 76, evaluate each exponential expression. (81x8y...
 P.P.1.70: In Exercises 63 to 74, use absolute value notation to describe the ...
 P.P.3.70: In Exercises 69 to 76, evaluate the given polynomial for the indica...
 P.70: In Exercises 59 to 72, simplify each radical expression. Assume tha...
 P.P.4.70: In Exercises 67 to 72, factor over the integers by grouping. a2y2 ...
 P.P.2.70: In Exercises 55 to 76, evaluate each exponential expression. (27x3y...
 P.P.1.71: In Exercises 63 to 74, use absolute value notation to describe the ...
 P.P.3.71: In Exercises 69 to 76, evaluate the given polynomial for the indica...
 P.71: In Exercises 59 to 72, simplify each radical expression. Assume tha...
 P.P.4.71: In Exercises 67 to 72, factor over the integers by grouping. 6w3 + ...
 P.P.2.71: In Exercises 55 to 76, evaluate each exponential expression. 16z3>5...
 P.P.1.72: In Exercises 63 to 74, use absolute value notation to describe the ...
 P.P.3.72: In Exercises 69 to 76, evaluate the given polynomial for the indica...
 P.72: In Exercises 59 to 72, simplify each radical expression. Assume tha...
 P.P.4.72: In Exercises 67 to 72, factor over the integers by grouping. 10z3 ...
 P.P.2.72: In Exercises 55 to 76, evaluate each exponential expression. 6a2>39...
 P.P.1.73: In Exercises 63 to 74, use absolute value notation to describe the ...
 P.P.3.73: In Exercises 69 to 76, evaluate the given polynomial for the indica...
 P.73: Write the polynomial 4x  7x2 + 5  x3 in standard form. Identify t...
 P.P.4.73: In Exercises 73 to 92, use the general factoring strategy to comple...
 P.P.2.73: In Exercises 55 to 76, evaluate each exponential expression. (2x2>3...
 P.P.1.74: In Exercises 63 to 74, use absolute value notation to describe the ...
 P.P.3.74: In Exercises 69 to 76, evaluate the given polynomial for the indica...
 P.74: Evaluate the polynomial 3x x = 2 3  4x2 + 2x  1 when x = 2.
 P.P.4.74: In Exercises 73 to 92, use the general factoring strategy to comple...
 P.P.2.74: In Exercises 55 to 76, evaluate each exponential expression. x1>3y5...
 P.P.1.75: In Exercises 75 to 82, evaluate the expression. 53 (4)2
 P.P.3.75: In Exercises 69 to 76, evaluate the given polynomial for the indica...
 P.75: In Exercises 75 to 82, perform the indicated operation and express ...
 P.P.4.75: In Exercises 73 to 92, use the general factoring strategy to comple...
 P.P.2.75: In Exercises 55 to 76, evaluate each exponential expression. 9a3>4b...
 P.P.1.76: In Exercises 75 to 82, evaluate the expression.  63(3)
 P.P.3.76: In Exercises 69 to 76, evaluate the given polynomial for the indica...
 P.76: In Exercises 75 to 82, perform the indicated operation and express ...
 P.P.4.76: In Exercises 73 to 92, use the general factoring strategy to comple...
 P.P.2.76: In Exercises 55 to 76, evaluate each exponential expression. 12x1>6...
 P.P.1.77: In Exercises 75 to 82, evaluate the expression. 4 + (3  8)2
 P.P.3.77: Recreation The air resistance (in pounds) on a cyclist riding a bic...
 P.77: In Exercises 75 to 82, perform the indicated operation and express ...
 P.P.4.77: In Exercises 73 to 92, use the general factoring strategy to comple...
 P.P.2.77: In Exercises 77 to 86, simplify each radical expression. 145
 P.P.1.78: In Exercises 75 to 82, evaluate the expression. 2 # 34  (6  7)6
 P.P.3.78: Highway Engineering On an expressway, the recommended safe distance...
 P.78: In Exercises 75 to 82, perform the indicated operation and express ...
 P.P.4.78: In Exercises 73 to 92, use the general factoring strategy to comple...
 P.P.2.78: In Exercises 77 to 86, simplify each radical expression. 175
 P.P.1.79: In Exercises 75 to 82, evaluate the expression. 28 , (7 + 5)
 P.P.3.79: Geometry The volume of a right circular cylinder (as shown below) i...
 P.79: In Exercises 75 to 82, perform the indicated operation and express ...
 P.P.4.79: In Exercises 73 to 92, use the general factoring strategy to comple...
 P.P.2.79: In Exercises 77 to 86, simplify each radical expression. 3 24
 P.P.1.80: In Exercises 75 to 82, evaluate the expression. (3  5)2(32  52
 P.P.3.80: Automotive Engineering The fuel efficiency (in miles per gallon of ...
 P.80: In Exercises 75 to 82, perform the indicated operation and express ...
 P.P.4.80: In Exercises 73 to 92, use the general factoring strategy to comple...
 P.P.2.80: In Exercises 77 to 86, simplify each radical expression. 3 1 135
 P.P.1.81: In Exercises 75 to 82, evaluate the expression. 7 + 233(2)3  42 , 84
 P.P.3.81: Psychology Based on data from one experiment, the reaction time, in...
 P.81: In Exercises 75 to 82, perform the indicated operation and express ...
 P.P.4.81: In Exercises 73 to 92, use the general factoring strategy to comple...
 P.P.2.81: In Exercises 77 to 86, simplify each radical expression. 3 135
 P.P.1.82: In Exercises 75 to 82, evaluate the expression. 5  433  6(2 # 32 ...
 P.P.3.82: Committee Membership The number of committees consisting of exactly...
 P.82: In Exercises 75 to 82, perform the indicated operation and express ...
 P.P.4.82: In Exercises 73 to 92, use the general factoring strategy to comple...
 P.P.2.82: In Exercises 77 to 86, simplify each radical expression. 3 1 250
 P.P.1.83: In Exercises 83 to 94, evaluate the variable expression for x 3, y ...
 P.P.3.83: Chess Matches Find the number of chess matches that can be played a...
 P.83: In Exercises 83 to 86, factor out the GCF. 12x3y4 + 10x2y3  34xy2
 P.P.4.83: In Exercises 73 to 92, use the general factoring strategy to comple...
 P.P.2.83: In Exercises 77 to 86, simplify each radical expression. 2 24x2y3
 P.P.1.84: In Exercises 83 to 94, evaluate the variable expression for x 3, y ...
 P.P.3.84: Computer Science A computer scientist determines that the time in s...
 P.84: In Exercises 83 to 86, factor out the GCF. 24a4b3 + 12a3b4  18a2b5
 P.P.4.84: In Exercises 73 to 92, use the general factoring strategy to comple...
 P.P.2.84: In Exercises 77 to 86, simplify each radical expression. 218x2y 2 5
 P.P.1.85: In Exercises 83 to 94, evaluate the variable expression for x 3, y ...
 P.P.3.85: Computer Science If is a positive integer, then which is read facto...
 P.85: In Exercises 83 to 86, factor out the GCF. (2x + 7)(3x  y)  (3x +...
 P.P.4.85: In Exercises 73 to 92, use the general factoring strategy to comple...
 P.P.2.85: In Exercises 77 to 86, simplify each radical expression. 3 7 16a3y7
 P.P.1.86: In Exercises 83 to 94, evaluate the variable expression for x 3, y ...
 P.P.3.86: Air Velocity of a Cough The velocity, in meters per second, of the ...
 P.86: In Exercises 83 to 86, factor out the GCF. (5x + 2)(3a  4)  (3a ...
 P.P.4.86: In Exercises 73 to 92, use the general factoring strategy to comple...
 P.P.2.86: In Exercises 77 to 86, simplify each radical expression. 3 54m2n 23 7
 P.P.1.87: In Exercises 83 to 94, evaluate the variable expression for x 3, y ...
 P.P.3.87: Sports The height, in feet, of a baseball released by a pitcher sec...
 P.87: In Exercises 87 to 102, factor the polynomial over the integers. x2...
 P.P.4.87: In Exercises 73 to 92, use the general factoring strategy to comple...
 P.P.2.87: In Exercises 87 to 94, simplify each radical and then combine like ...
 P.P.1.88: In Exercises 83 to 94, evaluate the variable expression for x 3, y ...
 P.P.3.88: Medicine The temperature, in degrees Fahrenheit, of a patient after...
 P.88: In Exercises 87 to 102, factor the polynomial over the integers. x2...
 P.P.4.88: In Exercises 73 to 92, use the general factoring strategy to comple...
 P.P.2.88: In Exercises 87 to 94, simplify each radical and then combine like ...
 P.P.1.89: In Exercises 83 to 94, evaluate the variable expression for x 3, y ...
 P.89: In Exercises 87 to 102, factor the polynomial over the integers. 2x...
 P.P.4.89: In Exercises 73 to 92, use the general factoring strategy to comple...
 P.P.2.89: In Exercises 87 to 94, simplify each radical and then combine like ...
 P.P.1.90: In Exercises 83 to 94, evaluate the variable expression for x 3, y ...
 P.90: In Exercises 87 to 102, factor the polynomial over the integers. 3x...
 P.P.4.90: In Exercises 73 to 92, use the general factoring strategy to comple...
 P.P.2.90: In Exercises 87 to 94, simplify each radical and then combine like ...
 P.P.1.91: In Exercises 83 to 94, evaluate the variable expression for x 3, y ...
 P.91: In Exercises 87 to 102, factor the polynomial over the integers. 6x...
 P.P.4.91: In Exercises 73 to 92, use the general factoring strategy to comple...
 P.P.2.91: In Exercises 87 to 94, simplify each radical and then combine like ...
 P.P.1.92: In Exercises 83 to 94, evaluate the variable expression for x 3, y ...
 P.92: In Exercises 87 to 102, factor the polynomial over the integers. 2...
 P.P.4.92: In Exercises 73 to 92, use the general factoring strategy to comple...
 P.P.2.92: In Exercises 87 to 94, simplify each radical and then combine like ...
 P.P.1.93: In Exercises 83 to 94, evaluate the variable expression for x 3, y ...
 P.93: In Exercises 87 to 102, factor the polynomial over the integers. 9x...
 P.P.4.93: In Exercises 93 and 94, find all positive values of k such that the...
 P.P.2.93: In Exercises 87 to 94, simplify each radical and then combine like ...
 P.P.1.94: In Exercises 83 to 94, evaluate the variable expression for x 3, y ...
 P.94: In Exercises 87 to 102, factor the polynomial over the integers. 25...
 P.P.4.94: In Exercises 93 and 94, find all positive values of k such that the...
 P.P.2.94: In Exercises 87 to 94, simplify each radical and then combine like ...
 P.P.1.95: In Exercises 95 to 108, state the property of real numbers or the p...
 P.95: In Exercises 87 to 102, factor the polynomial over the integers. x4...
 P.P.4.95: In Exercises 95 and 96, find k such that the trinomial is a perfect...
 P.P.2.95: In Exercises 95 to 104, find the indicated product and express each...
 P.P.1.96: In Exercises 95 to 108, state the property of real numbers or the p...
 P.96: In Exercises 87 to 102, factor the polynomial over the integers. x4...
 P.P.4.96: In Exercises 95 and 96, find k such that the trinomial is a perfect...
 P.P.2.96: In Exercises 95 to 104, find the indicated product and express each...
 P.P.1.97: In Exercises 95 to 108, state the property of real numbers or the p...
 P.97: In Exercises 87 to 102, factor the polynomial over the integers. x3...
 P.P.2.97: In Exercises 95 to 104, find the indicated product and express each...
 P.P.1.98: In Exercises 95 to 108, state the property of real numbers or the p...
 P.98: In Exercises 87 to 102, factor the polynomial over the integers. 3x...
 P.P.2.98: In Exercises 95 to 104, find the indicated product and express each...
 P.P.1.99: In Exercises 95 to 108, state the property of real numbers or the p...
 P.99: In Exercises 87 to 102, factor the polynomial over the integers. 4x...
 P.P.2.99: In Exercises 95 to 104, find the indicated product and express each...
 P.P.1.100: In Exercises 95 to 108, state the property of real numbers or the p...
 P.100: In Exercises 87 to 102, factor the polynomial over the integers. 2a...
 P.P.2.100: In Exercises 95 to 104, find the indicated product and express each...
 P.P.1.101: In Exercises 95 to 108, state the property of real numbers or the p...
 P.101: In Exercises 87 to 102, factor the polynomial over the integers. 24...
 P.P.2.101: In Exercises 95 to 104, find the indicated product and express each...
 P.P.1.102: In Exercises 95 to 108, state the property of real numbers or the p...
 P.102: In Exercises 87 to 102, factor the polynomial over the integers. 3x...
 P.P.2.102: In Exercises 95 to 104, find the indicated product and express each...
 P.P.1.103: In Exercises 95 to 108, state the property of real numbers or the p...
 P.103: In Exercises 103 and 104, simplify each rational expression. 6x2  ...
 P.P.2.103: In Exercises 95 to 104, find the indicated product and express each...
 P.P.1.104: In Exercises 95 to 108, state the property of real numbers or the p...
 P.104: In Exercises 103 and 104, simplify each rational expression. 4x3  ...
 P.P.2.104: In Exercises 95 to 104, find the indicated product and express each...
 P.P.1.105: In Exercises 95 to 108, state the property of real numbers or the p...
 P.105: In Exercises 105 to 108, perform the indicated operation and simpli...
 P.P.2.105: In Exercises 105 to 126, simplify each expression by rationalizing ...
 P.P.1.106: In Exercises 95 to 108, state the property of real numbers or the p...
 P.106: In Exercises 105 to 108, perform the indicated operation and simpli...
 P.P.2.106: In Exercises 105 to 126, simplify each expression by rationalizing ...
 P.P.1.107: In Exercises 95 to 108, state the property of real numbers or the p...
 P.107: In Exercises 105 to 108, perform the indicated operation and simpli...
 P.P.2.107: In Exercises 105 to 126, simplify each expression by rationalizing ...
 P.P.1.108: In Exercises 95 to 108, state the property of real numbers or the p...
 P.108: In Exercises 105 to 108, perform the indicated operation and simpli...
 P.P.2.108: In Exercises 105 to 126, simplify each expression by rationalizing ...
 P.P.1.109: Is division of real numbers an associative operation? Give a reason...
 P.109: In Exercises 109 and 110, simplify each complex fraction. 2 +1x  5...
 P.P.2.109: In Exercises 105 to 126, simplify each expression by rationalizing ...
 P.P.1.110: Is subtraction of real numbers a commutative operation? Give a reas...
 P.110: In Exercises 109 and 110, simplify each complex fraction. 2 +31 +4x
 P.P.2.110: In Exercises 105 to 126, simplify each expression by rationalizing ...
 P.P.1.111: Which of the properties of real numbers are satisfied by the integers?
 P.111: In Exercises 111 and 112, write the complex number in standard form...
 P.P.2.111: In Exercises 105 to 126, simplify each expression by rationalizing ...
 P.P.1.112: Which of the properties of real numbers are satisfied by the ration...
 P.112: In Exercises 111 and 112, write the complex number in standard form...
 P.P.2.112: In Exercises 105 to 126, simplify each expression by rationalizing ...
 P.P.1.113: In Exercises 113 to 122, simplify the variable expression. 2 + 3(2x...
 P.113: In Exercises 113 to 120, perform the indicated operation and write ...
 P.P.2.113: In Exercises 105 to 126, simplify each expression by rationalizing ...
 P.P.1.114: In Exercises 113 to 122, simplify the variable expression. 4 + 2(2a...
 P.114: In Exercises 113 to 120, perform the indicated operation and write ...
 P.P.2.114: In Exercises 105 to 126, simplify each expression by rationalizing ...
 P.P.1.115: In Exercises 113 to 122, simplify the variable expression. 5  3(4x...
 P.115: In Exercises 113 to 120, perform the indicated operation and write ...
 P.P.2.115: In Exercises 105 to 126, simplify each expression by rationalizing ...
 P.P.1.116: In Exercises 113 to 122, simplify the variable expression. 7  2(5n...
 P.116: In Exercises 113 to 120, perform the indicated operation and write ...
 P.P.2.116: In Exercises 105 to 126, simplify each expression by rationalizing ...
 P.P.1.117: In Exercises 113 to 122, simplify the variable expression. 3(2a  4...
 P.117: In Exercises 113 to 120, perform the indicated operation and write ...
 P.P.2.117: In Exercises 105 to 126, simplify each expression by rationalizing ...
 P.P.1.118: In Exercises 113 to 122, simplify the variable expression. 5(4r  7...
 P.118: In Exercises 113 to 120, perform the indicated operation and write ...
 P.P.2.118: In Exercises 105 to 126, simplify each expression by rationalizing ...
 P.P.1.119: In Exercises 113 to 122, simplify the variable expression. 5a  233...
 P.119: In Exercises 113 to 120, perform the indicated operation and write ...
 P.P.2.119: In Exercises 105 to 126, simplify each expression by rationalizing ...
 P.P.1.120: In Exercises 113 to 122, simplify the variable expression. 6 + 332x...
 P.120: In Exercises 113 to 120, perform the indicated operation and write ...
 P.P.2.120: In Exercises 105 to 126, simplify each expression by rationalizing ...
 P.P.1.121: In Exercises 113 to 122, simplify the variable expression. 34(5a + ...
 P.P.2.121: In Exercises 105 to 126, simplify each expression by rationalizing ...
 P.P.1.122: In Exercises 113 to 122, simplify the variable expression.  25(2x ...
 P.P.2.122: In Exercises 105 to 126, simplify each expression by rationalizing ...
 P.P.1.123: Area of a Triangle The area of a triangle is given by Area = 12bh w...
 P.P.2.123: In Exercises 105 to 126, simplify each expression by rationalizing ...
 P.P.1.124: Volume of a Box The volume of a rectangular box is given by Volume ...
 P.P.2.124: In Exercises 105 to 126, simplify each expression by rationalizing ...
 P.P.1.125: Heart Rate The heart rate, in beats per minute, of a certain runner...
 P.P.2.125: In Exercises 105 to 126, simplify each expression by rationalizing ...
 P.P.1.126: . Body Mass Index According to the National Institutes of Health, b...
 P.P.2.126: In Exercises 105 to 126, simplify each expression by rationalizing ...
 P.P.1.127: Physics The height, in feet, of a ball seconds after it is thrown u...
 P.P.2.127: In Exercises 127 and 128, rationalize the numerator, a technique th...
 P.P.1.128: Chemistry Salt is being added to water in such a way that the conce...
 P.P.2.128: In Exercises 127 and 128, rationalize the numerator, a technique th...
 P.P.2.129: Weight of an Orchid Seed An orchid seed weighs approximately 3.2 * ...
 P.P.2.130: Biology The weight of one E. coli baterium is approximately 670 fem...
 P.P.2.131: Doppler Effect Astronomers can approximate the distance to a galaxy...
 P.P.2.132: Laser Wavelength The wavelength of a certain heliumneon laser is 8...
 P.P.2.133: Astronomy The sun is approximately meters from Earth. If light trav...
 P.P.2.134: Astronomical Unit Earths mean distance from the sun is miles. This ...
 P.P.2.135: Mass of an Atom One gram of hydrogen contains 6.023 * 1023 atoms. F...
 P.P.2.136: Drug Potency The amount (in milligrams) of digoxin, a drug taken by...
 P.P.2.137: Oceanography The percent of light that will pass to a depth in mete...
 P.P.2.138: Learning Theory In a psychology experiment, students were given a n...
 P.P.2.139: Relativity Theory A moving object has energy, called kinetic energy...
Solutions for Chapter P: Preliminary Concepts
Full solutions for College Algebra  7th Edition
ISBN: 9781439048610
Solutions for Chapter P: Preliminary Concepts
Get Full SolutionsThis textbook survival guide was created for the textbook: College Algebra, edition: 7. Since 707 problems in chapter P: Preliminary Concepts have been answered, more than 25944 students have viewed full stepbystep solutions from this chapter. College Algebra was written by and is associated to the ISBN: 9781439048610. Chapter P: Preliminary Concepts includes 707 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

Iterative method.
A sequence of steps intended to approach the desired solution.

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)ยท(b  Ax) = o.

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.