 5.Review: (5.1) Evaluate. 222
 5.Cumulative Review: Find the roots.a. 23 27b. 25 1c. 24 16
 5.Test: Simplify. Use positive exponents to write the answers.1 9x22
 5.Test: Simplify. Use positive exponents to write the answers.3xy214xy22z
 5.Review: (5.1) Evaluate.1 324
 5.Cumulative Review: Find the roots.a. 23 64b. 24 81c. 25 32
 5.Test: Simplify. Use positive exponents to write the answers.61a2b332a5b2
 5.Review: (5.1) Evaluate.22
 5.Cumulative Review: Solve: 21x  32 = 5x  9.
 5.Test: Simplify. Use positive exponents to write the answers.axy5zxy3 b5
 5.Review: (5.1) Evaluate.34
 5.Cumulative Review: Solve: 0.3y + 2.4 = 0.1y + 4
 5.Test: Write Exercises 5 and 6 in scientific notation.630,000,000
 5.Review: (5.1) Evaluate.80
 5.Cumulative Review: Karen Estes just received an inheritance of $10,000 and plans to pl...
 5.Test: Write Exercises 5 and 6 in scientific notation.0.01200
 5.Review: (5.1) Evaluate.90
 5.Cumulative Review: A gallon of latex paint can cover 400 square feet. How many gallon ...
 5.Test: Write Exercises 5 and 6 in scientific notation.Write 5 * 106 witho...
 5.Review: (5.1) Evaluate.42
 5.Cumulative Review: Solve and graph the solution set. Write the solution set ininterval...
 5.Test: Write Exercises 5 and 6 in scientific notation.Use scientific notat...
 5.Review: (5.1) Evaluate.1 422
 5.Cumulative Review: Solve. Graph the solution set. Write the solution set in intervalno...
 5.Test: Perform the indicated operations14x3y  3x  42  19x3y + 8x + 52
 5.Review: Simplify each expression. Write each answer with positive exponents...
 5.Cumulative Review: Solve. 1 2x3+ 5 2
 5.Test: Perform the indicated operations 3xy14x + y2
 5.Review: Simplify each expression. Write each answer with positive exponents...
 5.Cumulative Review: Solve. 1363x + 1613
 5.Test: Perform the indicated operations 13x + 4214x  72
 5.Review: Simplify each expression. Write each answer with positive exponents...
 5.Cumulative Review: Solve.y 0 = 0
 5.Test: Perform the indicated operations15a  2b215a + 2b2
 5.Review: Simplify each expression. Write each answer with positive exponents...
 5.Cumulative Review: Solve.8 + 0 4c 0 = 24
 5.Test: Perform the indicated operations16m + n22
 5.Review: Simplify each expression. Write each answer with positive exponents...
 5.Cumulative Review: Solve.2x  110 ` 6 13
 5.Test: Perform the indicated operations12x  121x2  6x + 42
 5.Review: Simplify each expression. Write each answer with positive exponents...
 5.Cumulative Review: Solve.Solve: 0 5x  1 0 + 9 7 5
 5.Test: Factor each polynomial completely16x3y  12x2y4
 5.Review: Simplify each expression. Write each answer with positive exponents...
 5.Cumulative Review: Solve.Graph the linear equation y = 13x.
 5.Test: Factor each polynomial completelyx2  13x  30
 5.Cumulative Review: Solve.Graph the linear equation y = 3x.
 5.Review: Simplify each expression. Write each answer with positive exponents...
 5.Test: Factor each polynomial completely4y2 + 20y + 25
 5.Review: Write in scientific notation.36,890,000
 5.Cumulative Review: Solve.Evaluate f 122, f 1 62, and f 102 for the functionf 1x2 = e ...
 5.Test: Factor each polynomial completely6x2  15x  9
 5.Cumulative Review: Solve.If f 1x2 = 3x2 + 2x + 3, find f 1 32 .
 5.Review: Write in scientific notation.0.000362
 5.Test: Factor each polynomial completely4x2  25
 5.Cumulative Review: Solve.Graph x = 2.
 5.Review: Write each number in standard notation, without exponents.1.678 * 106
 5.Test: Factor each polynomial completelyx3 + 64
 5.Cumulative Review: Solve.Graph y  5 = 0
 5.Review: Write each number in standard notation, without exponents.4.1 * 105
 5.Test: Factor each polynomial completely3x2y  27y3
 5.Cumulative Review: Solve.Find the slope of the line y = 2.
 5.Review: (5.2) Simplify. Use only positive exponents18523
 5.Test: Factor each polynomial completely6x2 + 24
 5.Cumulative Review: Solve.Find the slope of the line f 1x2 = 2x  3.
 5.Review: (5.2) Simplify. Use only positive exponentsaa4b2
 5.Test: Factor each polynomial completely16y3  2
 5.Cumulative Review: Solve.Find an equation of the horizontal line containing the point(...
 5.Review: (5.2) Simplify. Use only positive exponents13x23
 5.Test: Factor each polynomial completelyx2y  9y  3x2 + 27
 5.Cumulative Review: Solve.Find the equation of the vertical line containing the point1 ...
 5.Review: (5.2) Simplify. Use only positive exponents1 4x22
 5.Test: Solve the equation for the variable.3n17n  202 = 96
 5.Cumulative Review: Solve.Graph the union of x +12y 4 or y 2.
 5.Review: (5.2) Simplify. Use only positive exponentsa6x5 b2
 5.Test: Solve the equation for the variable.1x + 221x  22 = 51x + 42
 5.Cumulative Review: Solve.Find the equation of the line containing the point 1 2, 32an...
 5.Review: (5.2) Simplify. Use only positive exponents18623
 5.Test: Solve the equation for the variable.2x3 + 5x2 = 8x + 20
 5.Cumulative Review: Solve.Use the substitution method to solve the system.e2x + 4y = 6...
 5.Review: (5.2) Simplify. Use only positive exponentsa43b2
 5.Test: Solve the equation for the variable.Write the area of the shaded re...
 5.Cumulative Review: Solve.Use the substitution method to solve the system.e4x  2y = 8y...
 5.Review: (5.2) Simplify. Use only positive exponents 2x323
 5.Test: Solve the equation for the variable.A pebble is hurled upward from ...
 5.Cumulative Review: Solve.Solve the system. 2x + 4y = 14x  4z = 1y  4z = 3
 5.Review: (5.2) Simplify. Use only positive exponentsa8p64p4 b2
 5.Cumulative Review: Solve.Solve the system. ex + y  32z = 12y  2z = 14x  23y =  13
 5.Review: (5.2) Simplify. Use only positive exponents1 3x2y223
 5.Cumulative Review: Solve.A first number is 4 less than a second number. Four timesthe ...
 5.Review: (5.2) Simplify. Use only positive exponents ax5y3z3 b5
 5.Cumulative Review: Solve.One solution contains 20% acid and a second solution contains...
 5.Review: (5.2) Simplify. Use only positive exponents41x3yzx2yx4
 5.Cumulative Review: Solve.Use matrices to solve the system. e2x  y = 34x  2y = 5
 5.Review: (5.2) Simplify. Use only positive exponents15xyz241x223
 5.Cumulative Review: Solve.Use matrices to solve the system. e 4y = 8x + y = 7
 5.Review: (5.2) Simplify. Use only positive exponents213yz23y3
 5.Cumulative Review: Solve.The measure of the largest angle of a triangle is 80 morethan...
 5.Review: Simplify each expressionx4a13x5a23
 5.Cumulative Review: Solve.Find an equation of the line with slope 12 through the point ...
 5.Review: Simplify each expression4y3x32y2x+4
 5.Cumulative Review: Solve.Write each number in scientific notation.a. 730,000b. 0.00000104
 5.Review: Use scientific notation to find the quotient. Express each quotient...
 5.Cumulative Review: Solve.Write each number in scientific notation.a. 8,250,000b. 0.000...
 5.Review: Use scientific notation to find the quotient. Express each quotient...
 5.Cumulative Review: Solve.Simplify each expression. Use positive exponents to writethe ...
 5.Review: Simplify. Use only positive exponents.27x5y518x6y2#x4y2x2y3
 5.Cumulative Review: Solve.Simplify each expression. Use positive exponents to writethe ...
 5.Review: Simplify. Use only positive exponents.3x5y4 #13xy3221z324
 5.Cumulative Review: Solve.Find the degree of the polynomial 3xy + x2y2  5x2  6.7.
 5.Review: (5.3) Find the degree of each polynomial.x2y  3xy3z + 5x + 7y
 5.Cumulative Review: Solve.Subtract 15x2 + 3x2 from 13x2  2x2 .
 5.Review: (5.3) Find the degree of each polynomial.3x + 2
 5.Cumulative Review: Solve.Multiply.a. 12x3215x62b. 17y4z421 xy11z52
 5.Review: Simplify by combining like terms.4x + 8x  6x2  6x2y
 5.Cumulative Review: Solve.Multiply.a. 13y6214y22b. 16a3b221 a2bc 42
 5.Review: Simplify by combining like terms.8xy3 + 4xy3  3x3y
 5.Cumulative Review: Factor.17x3y2  34x4y2
 5.Review: Add or subtract as indicated.13x + 7y2 + 14x2  3x + 72 + 1y  12
 5.Cumulative Review: Factor.12x3y  3xy3
 5.Review: Add or subtract as indicated. 14x2  6xy + 9y22  18x2  6xy  y22
 5.Cumulative Review: Factor.x2 + 10x + 16
 5.Review: Add or subtract as indicated. 13x2  4b + 282 + 19x2  302  14x2 ...
 5.Cumulative Review: Factor.5a2 + 14a  3
 5.Review: Add or subtract as indicated.Add 19xy + 4x2 + 182 and 17xy  4x3  ...
 5.Cumulative Review: Solve2x2 + 9x  5 = 0
 5.Review: Add or subtract as indicated. Substract 13x  52 from 2x
 5.Cumulative Review: Solve3x2  10x  8 = 0
 5.Review: Add or subtract as indicated.Subtract 1x  72 from the sum of 13x2y...
 5.Review: Add or subtract as indicated.x2  5x + 7(x + 4)
 5.Review: Add or subtract as indicated.x3 + 2xy2  y+ 1x  4xy2  72
 5.Review: If P1x2 = 9x2  7x + 8, find the following.P(6)
 5.Review: If P1x2 = 9x2  7x + 8, find the following.P(0)
 5.Review: If P1x2 = 9x2  7x + 8, find the following.P1 22
 5.Review: If P1x2 = 9x2  7x + 8, find the following.P1 32
 5.Review: If P1x2 = 2x  1 and Q1x2 = x2 + 2x  5, find the followingP1x2 + Q1x2
 5.Review: If P1x2 = 2x  1 and Q1x2 = x2 + 2x  5, find the following2 # P1x2...
 5.Review: Find the perimeter of the rectangle.2x2y 6x 1cm
 5.Review: Find the perimeter of the triangle.(3x 11) in.3x in.(
 5.Review: (5.4) Multiply.6x14x2  6x + 12
 5.Review: (5.4) Multiply.4ab213ab3 + 7ab + 12
 5.Review: (5.4) Multiply. 1x  4212x + 92
 5.Review: (5.4) Multiply. 1 3xa + 4b22
 5.Review: (5.4) Multiply.19x2 + 4x + 1214x  32
 5.Review: (5.4) Multiply.12x  121x2 + 2x  52
 5.Review: (5.4) Multiply.15x  9y213x + 9y2
 5.Review: (5.4) Multiply.ax  13b ax +23b
 5.Review: (5.4) Multiply.1x2 + 9x + 122
 5.Review: (5.4) Multiply.1m2 + m  222
 5.Review: Multiply, using special products.13x  y22
 5.Review: Multiply, using special products.14x + 922
 5.Review: Multiply, using special products.1x + 3y21x  3y2
 5.Review: Multiply, using special products.[4 + 13a  b2][4  13a  b2]
 5.Review: Find the area of the rectangle.
 5.Review: Find the area of the square.
 5.Review: Multiply. Assume that all variable exponents represent integers.4ab...
 5.Review: Multiply. Assume that all variable exponents represent integers.13x...
 5.Review: (5.5) Factor out the greatest common factor.16x3  24x2
 5.Review: (5.5) Factor out the greatest common factor.36y  24y2
 5.Review: (5.5) Factor out the greatest common factor.6ab2 + 8ab  4a2b2
 5.Review: (5.5) Factor out the greatest common factor.14a2b2  21ab2 + 7ab
 5.Review: (5.5) Factor out the greatest common factor.6a1a + 3b2  51a + 3b2
 5.Review: (5.5) Factor out the greatest common factor.4x1x  2y2  51x  2y2
 5.Review: Factor by grouping.xy  6y + 3x  18
 5.Review: Factor by grouping.xy  6y + 3x  18
 5.Review: Factor by grouping.pq  3p  5q + 15
 5.Review: Factor by grouping.x3  x2  2x + 2
 5.Review: For Exercises 89 and 90, smaller squares are cut from larger rectan...
 5.Review: For Exercises 89 and 90, smaller squares are cut from larger rectan...
 5.Review: (5.6) Completely factor each polynomial.x2  14x  72
 5.Review: (5.6) Completely factor each polynomial.x2 + 16x  80
 5.Review: (5.6) Completely factor each polynomial.2x2  18x + 28
 5.Review: (5.6) Completely factor each polynomial.3x2 + 33x + 54
 5.Review: (5.6) Completely factor each polynomial.2x3  7x2  9x
 5.Review: (5.6) Completely factor each polynomial.3x3 + 2x2  16x
 5.Review: (5.6) Completely factor each polynomial.6x2 + 17x + 10
 5.Review: (5.6) Completely factor each polynomial.15x2  91x + 6
 5.Review: (5.6) Completely factor each polynomial.4x2 + 2x  12
 5.Review: (5.6) Completely factor each polynomial.9x2  12x  12
 5.Review: (5.6) Completely factor each polynomial.y21x + 622  2y1x + 622  3...
 5.Review: (5.6) Completely factor each polynomial.1x + 522 + 61x + 52 + 8
 5.Review: (5.6) Completely factor each polynomial.x4  6x2  16
 5.Review: (5.6) Completely factor each polynomial.x4 + 8x2  20
 5.Review: (5.7) Factor each polynomial completelyx2  100
 5.Review: (5.7) Factor each polynomial completelyx2  81
 5.Review: (5.7) Factor each polynomial completely2x2  32
 5.Review: (5.7) Factor each polynomial completely6x2  54
 5.Review: (5.7) Factor each polynomial completely81  x4
 5.Review: (5.7) Factor each polynomial completely16  y4
 5.Review: (5.7) Factor each polynomial completely1y + 222  25
 5.Review: (5.7) Factor each polynomial completely1x  322  16
 5.Review: (5.7) Factor each polynomial completelyx3 + 216
 5.Review: (5.7) Factor each polynomial completelyy3 + 512
 5.Review: (5.7) Factor each polynomial completely8  27y3
 5.Review: (5.7) Factor each polynomial completely1  64y3
 5.Review: (5.7) Factor each polynomial completely6x4y + 48xy
 5.Review: (5.7) Factor each polynomial completely2x5 + 16x2y3
 5.Review: (5.7) Factor each polynomial completelyx2  2x + 1  y2
 5.Review: (5.7) Factor each polynomial completelyx2  6x + 9  4y2
 5.Review: (5.7) Factor each polynomial completely4x2 + 12x + 9
 5.Review: (5.7) Factor each polynomial completely16a2  40ab + 25b2
 5.Review: The volume of the cylindrical shell is 1pR2 h  pr2 h2 cubic units....
 5.Review: The surface area of the cylindrical shell (except for its topand bo...
 5.Review: (5.8) Solve each polynomial equation for the variable.13x  121x + ...
 5.Review: (5.8) Solve each polynomial equation for the variable.31x + 5218x ...
 5.Review: (5.8) Solve each polynomial equation for the variable.5x1x  4212x ...
 5.Review: (5.8) Solve each polynomial equation for the variable.61x + 321x  ...
 5.Review: (5.8) Solve each polynomial equation for the variable.2x2 = 12x
 5.Review: (5.8) Solve each polynomial equation for the variable.4x3  36x = 0
 5.Review: (5.8) Solve each polynomial equation for the variable.11  x213x + ...
 5.Review: (5.8) Solve each polynomial equation for the variable.2x1x  122 = 40
 5.Review: (5.8) Solve each polynomial equation for the variable.3x2 + 2x = 12...
 5.Review: (5.8) Solve each polynomial equation for the variable.2x2 + 3x = 35
 5.Review: (5.8) Solve each polynomial equation for the variable.x3  18x = 3x2
 5.Review: (5.8) Solve each polynomial equation for the variable.19x2  42x = x3
 5.Review: (5.8) Solve each polynomial equation for the variable.12x = 6x3 + 6x2
 5.Review: (5.8) Solve each polynomial equation for the variable.8x3 + 10x2 = 3x
 5.Review: (5.8) Solve each polynomial equation for the variable.The sum of a ...
 5.Review: (5.8) Solve each polynomial equation for the variable.The length of...
 5.Review: (5.8) Solve each polynomial equation for the variable.A scene from ...
 5.Review: (5.8) Solve each polynomial equation for the variable.The Royal Gor...
 5.Review: Perform the indicated operation.1x + 5213x2  2x + 12
 5.Review: Perform the indicated operation.13x2 + 4x  1.22  15x2  x + 5.72
 5.Review: Perform the indicated operation.13x2 + 4x  1.22 + 15x2  x + 5.72
 5.Review: Perform the indicated operation.a7ab  12b2
 5.Review: If P1x2 = x2 + x  4, findP152
 5.Review: If P1x2 = x2 + x  4, findP1 22
 5.Review: Factor each polynomial completely.12y5  6y4
 5.Review: Factor each polynomial completely.x2y + 4x2  3y  12
 5.Review: Factor each polynomial completely.6x2  34x  12
 5.Review: Factor each polynomial completely.y214x + 322  19y14x + 322  2014...
 5.Review: Factor each polynomial completely.4z7  49z5
 5.Review: Factor each polynomial completely.5x4 + 4x2  9
 5.Review: Solve each equation8x2 = 24x
 5.Review: Solve each equationx1x  112 = 26
Solutions for Chapter 5: Exponents, Polynomials, and Polynomial Functions
Full solutions for Intermediate Algebra  6th Edition
ISBN: 9780321785046
Solutions for Chapter 5: Exponents, Polynomials, and Polynomial Functions
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Intermediate Algebra, edition: 6. Chapter 5: Exponents, Polynomials, and Polynomial Functions includes 235 full stepbystep solutions. Intermediate Algebra was written by and is associated to the ISBN: 9780321785046. Since 235 problems in chapter 5: Exponents, Polynomials, and Polynomial Functions have been answered, more than 60056 students have viewed full stepbystep solutions from this chapter.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

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

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

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

Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

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

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.