 5.2.1: To multiply the variables in monomials, retain each variable and __...
 5.2.2: To multiply 7x3 (4x5  8x2 + 6), use the ______________ property to...
 5.2.3: To multiply (5x + 3)(x2 + 8x + 7), begin by multiplying each term o...
 5.2.4: When using the FOIL method to find (x + 7)(3x + 5), the product of ...
 5.2.5: (A + B) 2 = ______________. The square of a binomial sum is the fir...
 5.2.6: (A  B) 2 = ______________. The square of a binomial difference is ...
 5.2.7: (A + B)(A  B) = ______________. The product of the sum and differe...
 5.2.8: If f(x) = x2  4x + 7, we find f(a + h) by replacing each occurrenc...
 5.2.9: 4x2 (3x + 2)
 5.2.10: 5x2 (6x + 7)
 5.2.11: 2y(y2  5y)
 5.2.12: 3y(y2  4y)
 5.2.13: 5x3 (2x5  4x2 + 9)
 5.2.14: 6x3 (3x5  5x2 + 7)
 5.2.15: 4xy(7x + 3y)
 5.2.16: 5xy(8x + 3y)
 5.2.17: 3ab2 (6a2b3 + 5ab)
 5.2.18: 5ab2 (10a2b3 + 7ab)
 5.2.19: 4x2y(3x4y2  7xy3 + 6)
 5.2.20: 3x2y(10x2y4  2xy3 + 7)
 5.2.21: 4xna3x2n  5xn + 1 2 xb
 5.2.22: 10xna4x2n  3xn + 1 5 xb
 5.2.23: (x  3)(x2 + 2x + 5)
 5.2.24: (x + 4)(x2  5x + 8)
 5.2.25: (x  1)(x2 + x + 1)
 5.2.26: (x  2)(x2 + 2x + 4)
 5.2.27: (a  b)(a2 + ab + b2 )
 5.2.28: (a + b)(a2  ab + b2 )
 5.2.29: (x2 + 2x  1)(x2 + 3x  4)
 5.2.30: (x2  2x + 3)(x2 + x + 1)
 5.2.31: (x  y)(x2  3xy + y2 )
 5.2.32: (x  y)(x2  4xy + y2 )
 5.2.33: (xy + 2)(x2y2  2xy + 4)
 5.2.34: (xy + 3)(x2y2  2xy + 5)
 5.2.35: (x + 4)(x + 7)
 5.2.36: (x + 5)(x + 8)
 5.2.37: (y + 5)(y  6)
 5.2.38: (y + 5)(y  8)
 5.2.39: (5x + 3)(2x + 1)
 5.2.40: (4x + 3)(5x + 1)
 5.2.41: (3y  4)(2y  1)
 5.2.42: (5y  2)(3y  1)
 5.2.43: (3x  2)(5x  4)
 5.2.44: (2x  3)(4x  5)
 5.2.45: (x  3y)(2x + 7y)
 5.2.46: (3x  y)(2x + 5y)
 5.2.47: (7xy + 1)(2xy  3)
 5.2.48: (3xy  1)(5xy + 2)
 5.2.49: (x  4)(x2  5)
 5.2.50: (x  5)(x2  3)
 5.2.51: (8x3 + 3)(x2  5)
 5.2.52: (7x3 + 5)(x2  2)
 5.2.53: (3xn  yn )(xn + 2yn )
 5.2.54: (5xn  yn )(xn + 4yn )
 5.2.55: (x + 3) 2
 5.2.56: (x + 4) 2
 5.2.57: (y  5) 2
 5.2.58: (y  6) 2
 5.2.59: (2x + y) 2
 5.2.60: (4x + y) 2
 5.2.61: (5x  3y) 2
 5.2.62: (3x  4y) 2
 5.2.63: (2x2 + 3y) 2
 5.2.64: (4x2 + 5y) 2
 5.2.65: (4xy2  xy) 2
 5.2.66: (5xy2  xy) 2
 5.2.67: (an + 4bn ) 2
 5.2.68: (3an  bn ) 2
 5.2.69: (x + 4)(x  4)
 5.2.70: (x + 5)(x  5)
 5.2.71: (5x + 3)(5x  3)
 5.2.72: (3x + 2)(3x  2)
 5.2.73: (4x + 7y)(4x  7y)
 5.2.74: (8x + 7y)(8x  7y)
 5.2.75: (y3 + 2)(y3  2)
 5.2.76: (y3 + 3)(y3  3)
 5.2.77: (1  y5 )(1 + y5 )
 5.2.78: (2  y5 )(2 + y5 )
 5.2.79: (7xy2  10y)(7xy2 + 10y)
 5.2.80: (3xy2  4y)(3xy2 + 4y)
 5.2.81: (5an  7)(5an + 7)
 5.2.82: (10bn  3)(10bn + 3)
 5.2.83: [(2x + 3) + 4y][(2x + 3)  4y]
 5.2.84: [(3x + 2) + 5y][(3x + 2)  5y]
 5.2.85: (x + y + 3)(x + y  3)
 5.2.86: (x + y + 4)(x + y  4)
 5.2.87: (5x + 7y  2)(5x + 7y + 2)
 5.2.88: (7x + 5y  2)(7x + 5y + 2)
 5.2.89: [5y + (2x + 3)][5y  (2x + 3)]
 5.2.90: [8y + (3x + 2)][8y  (3x + 2)]
 5.2.91: (x + y + 1) 2
 5.2.92: (x + y + 2) 2
 5.2.93: (x + 1)(x  1)(x2 + 1)
 5.2.94: (x + 2)(x  2)(x2 + 4)
 5.2.95: Let f(x) = x  2 and g(x) = x + 6. Find each of the following. a. (...
 5.2.96: Let f(x) = x  4 and g(x) = x + 10. Find each of the following. a. ...
 5.2.97: Let f(x) = x  3 and g(x) = x2 + 3x + 9. Find each of the following...
 5.2.98: Let f(x) = x + 3 and g(x) = x2  3x + 9. Find each of the following...
 5.2.99: f(x) = x2  3x + 7
 5.2.100: f(x) = x2  4x + 9
 5.2.101: f(x) = 3x2 + 2x  1
 5.2.102: f(x) = 4x2 + 5x  1
 5.2.103: (3x + 4y) 2  (3x  4y) 2
 5.2.104: (5x + 2y) 2  (5x  2y) 2
 5.2.105: (5x  7)(3x  2)  (4x  5)(6x  1)
 5.2.106: (3x + 5)(2x  9)  (7x  2)(x  1)
 5.2.107: (2x + 5)(2x  5)(4x2 + 25)
 5.2.108: (3x + 4)(3x  4)(9x2 + 16)
 5.2.109: (x  1) 3
 5.2.110: (x  2) 3
 5.2.111: (2x  7) 5 (2x  7) 3
 5.2.112: (5x  3) 6 (5x  3) 4
 5.2.113: In Exercises 113114, find the area of the large rectangle in two wa...
 5.2.114: In Exercises 113114, find the area of the large rectangle in two wa...
 5.2.115: In Exercises 115116, express each polynomial in standard formthat i...
 5.2.116: In Exercises 115116, express each polynomial in standard formthat i...
 5.2.117: In Exercises 117118, express each polynomial in standard form. a. W...
 5.2.118: In Exercises 117118, express each polynomial in standard form. a. W...
 5.2.119: A popular model of carryon luggage has a length that is 10 inches ...
 5.2.120: Before working this exercise, be sure that you have read the Blitze...
 5.2.121: Explain how to multiply monomials. Give an example.
 5.2.122: Explain how to multiply a monomial and a polynomial that is not a m...
 5.2.123: Explain how to multiply a binomial and a trinomial.
 5.2.124: What is the FOIL method and when is it used? Give an example of the...
 5.2.125: Explain how to square a binomial sum. Give an example.
 5.2.126: Explain how to square a binomial difference. Give an example.
 5.2.127: Explain how to find the product of the sum and difference of two te...
 5.2.128: How can the graph of function f g be obtained from the graphs of fu...
 5.2.129: Explain how to find f(a + h)  f(a) for a given function f.
 5.2.130: y1 = (x  2) 2 y2 = x2  4x + 4
 5.2.131: y1 = (x  4)(x2  3x + 2) y2 = x3  7x2 + 14x  8
 5.2.132: y1 = (x  1)(x2 + x + 1) y2 = x3  1
 5.2.133: y1 = (x + 1.5)(x  1.5) y2 = x2  2.25
 5.2.134: Graph f(x) = x + 4, g(x) = x  2, and the product function, f g, in...
 5.2.135: Knowing the difference between factors and terms is important: In (...
 5.2.136: I used the FOIL method to find the product of x + 5 and x2 + 2x + 1.
 5.2.137: Instead of using the formula for the square of a binomial sum, I pr...
 5.2.138: Specialproduct formulas have patterns that make their multiplicati...
 5.2.139: If f is a polynomial function, then f(a + h)  f(a) = f(a) + f(h) ...
 5.2.140: (x  5) 2 = x2  5x + 25
 5.2.141: (x + 1) 2 = x2 + 1
 5.2.142: Suppose a square garden has an area represented by 9x2 square feet....
 5.2.143: Express the area of the plane figure shown as a polynomial in stand...
 5.2.144: In Exercises 144145, represent the volume of each figure as a polyn...
 5.2.145: In Exercises 144145, represent the volume of each figure as a polyn...
 5.2.146: Simplify: (yn + 2)(yn  2)  (yn  3)2 .
 5.2.147: The product of two consecutive odd integers is 22 less than the squ...
 5.2.148: Solve: 3x + 4 10. (Section 4.3, Example 6)
 5.2.149: Solve: 2  6x 20. (Section 4.1, Example 2)
 5.2.150: Write in scientific notation: 8,034,000,000. (Section 1.7, Example 2)
 5.2.151: Replace each boxed question mark with a polynomial that results in ...
 5.2.152: (x  5)(x2 + 3)
 5.2.153: (x + 4)(3x  2y)
Solutions for Chapter 5.2: Multiplication of Polynomials
Full solutions for Intermediate Algebra for College Students  6th Edition
ISBN: 9780321758934
Solutions for Chapter 5.2: Multiplication of Polynomials
Get Full SolutionsIntermediate Algebra for College Students was written by and is associated to the ISBN: 9780321758934. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Intermediate Algebra for College Students, edition: 6. Since 153 problems in chapter 5.2: Multiplication of Polynomials have been answered, more than 22181 students have viewed full stepbystep solutions from this chapter. Chapter 5.2: Multiplication of Polynomials includes 153 full stepbystep solutions.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , AjIb. Numerical methods approximate A I b by x j with residual b  Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

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

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).