 8.5.1: We solve the polynomial inequality x2 + 8x + 15 7 0 by first solvin...
 8.5.2: The points at 5 and 3 shown above divide the number line into thr...
 8.5.3: True or false: A test value for the leftmost interval on the number...
 8.5.4: True or false: A test value for the rightmost interval on the numbe...
 8.5.5: Consider the rational inequality x  1 x + 2 0. Setting the numerat...
 8.5.6: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.7: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.8: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.9: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.10: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.11: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.12: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.13: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.14: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.15: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.16: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.17: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.18: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.19: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.20: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.21: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.22: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.23: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.24: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.25: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.26: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.27: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.28: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.29: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.30: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.31: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.32: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.33: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.34: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.35: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.36: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.37: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.38: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.39: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.40: Solve each polynomial inequality in Exercises 140 and graph the sol...
 8.5.41: Solve each rational inequality in Exercises 4156 and graph the solu...
 8.5.42: Solve each rational inequality in Exercises 4156 and graph the solu...
 8.5.43: Solve each rational inequality in Exercises 4156 and graph the solu...
 8.5.44: Solve each rational inequality in Exercises 4156 and graph the solu...
 8.5.45: Solve each rational inequality in Exercises 4156 and graph the solu...
 8.5.46: Solve each rational inequality in Exercises 4156 and graph the solu...
 8.5.47: Solve each rational inequality in Exercises 4156 and graph the solu...
 8.5.48: Solve each rational inequality in Exercises 4156 and graph the solu...
 8.5.49: Solve each rational inequality in Exercises 4156 and graph the solu...
 8.5.50: Solve each rational inequality in Exercises 4156 and graph the solu...
 8.5.51: Solve each rational inequality in Exercises 4156 and graph the solu...
 8.5.52: Solve each rational inequality in Exercises 4156 and graph the solu...
 8.5.53: Solve each rational inequality in Exercises 4156 and graph the solu...
 8.5.54: Solve each rational inequality in Exercises 4156 and graph the solu...
 8.5.55: Solve each rational inequality in Exercises 4156 and graph the solu...
 8.5.56: Solve each rational inequality in Exercises 4156 and graph the solu...
 8.5.57: In Exercises 5760, use the given functions to find all values of x ...
 8.5.58: In Exercises 5760, use the given functions to find all values of x ...
 8.5.59: In Exercises 5760, use the given functions to find all values of x ...
 8.5.60: In Exercises 5760, use the given functions to find all values of x ...
 8.5.61: Solve each inequality in Exercises 6166 and graph the solution set ...
 8.5.62: Solve each inequality in Exercises 6166 and graph the solution set ...
 8.5.63: Solve each inequality in Exercises 6166 and graph the solution set ...
 8.5.64: Solve each inequality in Exercises 6166 and graph the solution set ...
 8.5.65: Solve each inequality in Exercises 6166 and graph the solution set ...
 8.5.66: Solve each inequality in Exercises 6166 and graph the solution set ...
 8.5.67: In Exercises 6768, use the graph of the polynomial function to solv...
 8.5.68: In Exercises 6768, use the graph of the polynomial function to solv...
 8.5.69: In Exercises 6970, use the graph of the rational function to solve ...
 8.5.70: In Exercises 6970, use the graph of the rational function to solve ...
 8.5.71: You throw a ball straight up from a rooftop 160 feet high with an i...
 8.5.72: Divers in Acapulco, Mexico, dive headfirst from the top of a cliff ...
 8.5.73: a. Use the given functions to find the stopping distance on dry pav...
 8.5.74: a. Use the given functions to find the stopping distance on dry pav...
 8.5.75: Describe the companys production level so that the average cost of ...
 8.5.76: Describe the companys production level so that the average cost of ...
 8.5.77: The perimeter of a rectangle is 50 feet. Describe the possible leng...
 8.5.78: The perimeter of a rectangle is 180 feet. Describe the possible len...
 8.5.79: What is a polynomial inequality?
 8.5.80: What is a rational inequality?
 8.5.81: Describe similarities and differences between the solutions of (x ...
 8.5.82: Solve each inequality in Exercises 8287 using a graphing utilityx2 ...
 8.5.83: Solve each inequality in Exercises 8287 using a graphing utility2x2...
 8.5.84: Solve each inequality in Exercises 8287 using a graphing utility x ...
 8.5.85: Solve each inequality in Exercises 8287 using a graphing utility x ...
 8.5.86: Solve each inequality in Exercises 8287 using a graphing utility 1x...
 8.5.87: Solve each inequality in Exercises 8287 using a graphing utility x3...
 8.5.88: The graph shows stopping distances for trucks at various speeds on ...
 8.5.89: The graph shows stopping distances for trucks at various speeds on ...
 8.5.90: Make Sense? In Exercises 9093, determine whether each statement mak...
 8.5.91: Make Sense? In Exercises 9093, determine whether each statement mak...
 8.5.92: Make Sense? In Exercises 9093, determine whether each statement mak...
 8.5.93: Make Sense? In Exercises 9093, determine whether each statement mak...
 8.5.94: In Exercises 9497, determine whether each statement is true or fals...
 8.5.95: In Exercises 9497, determine whether each statement is true or fals...
 8.5.96: In Exercises 9497, determine whether each statement is true or fals...
 8.5.97: In Exercises 9497, determine whether each statement is true or fals...
 8.5.98: Write a quadratic inequality whose solution set is [3, 5]
 8.5.99: Write a rational inequality whose solution set is ( , 4) [3, ).
 8.5.100: In Exercises 100103, use inspection to describe each inequalitys so...
 8.5.101: In Exercises 100103, use inspection to describe each inequalitys so...
 8.5.102: In Exercises 100103, use inspection to describe each inequalitys so...
 8.5.103: In Exercises 100103, use inspection to describe each inequalitys so...
 8.5.104: The graphing calculator screen shows the graph of y = 4x2  8x + 7....
 8.5.105: The graphing calculator screen shows the graph of y = 227  3x2 . W...
 8.5.106: Solve: 2 x  5 3 2 6 8. (Section 4.3, Example 4)
 8.5.107: Divide: 2x + 6 x2 + 8x + 16 , x2  9 x2 + 3x  4 . (Section 6.1, Ex...
 8.5.108: Factor completely: x4  16y4 . (Section 5.5, Example 3)
 8.5.109: Exercises 109111 will help you prepare for the material covered in ...
 8.5.110: Exercises 109111 will help you prepare for the material covered in ...
 8.5.111: Exercises 109111 will help you prepare for the material covered in ...
Solutions for Chapter 8.5: Polynomial and Rational Inequalities
Full solutions for Intermediate Algebra for College Students  6th Edition
ISBN: 9780321758934
Solutions for Chapter 8.5: Polynomial and Rational Inequalities
Get Full SolutionsChapter 8.5: Polynomial and Rational Inequalities includes 111 full stepbystep solutions. Since 111 problems in chapter 8.5: Polynomial and Rational Inequalities have been answered, more than 29687 students have viewed full stepbystep solutions from this chapter. Intermediate 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.

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

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

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

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.

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

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

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

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

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

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.