 5.5.1: Findf1x2 = 2x2 f112  x
 5.5.2: actor the expression 6x 2 + x  2
 5.5.3: Find the quotient and remainder if 3x4  5x3 + 7x  4 is divided by
 5.5.4: Find the zeros off1x2 = x 2 + x  3
 5.5.5: In the process of polynomial division,1Divisor21Quotient2 +
 5.5.6: When a polynomial function f is divided by , the remainder i
 5.5.7: If a function f, whose domain is all real numbers, is even and if 4...
 5.5.8: True or False Every polynomial function of degree 3 with real coeff...
 5.5.9: If f is a polynomial function and is a factor of f, thenf142 =
 5.5.10: True or False If f is a polynomial function of degree 4 and if , th...
 5.5.11: In 1120, use the Remainder Theorem to find the remainder when is di...
 5.5.12: In 1120, use the Remainder Theorem to find the remainder when is di...
 5.5.13: In 1120, use the Remainder Theorem to find the remainder when is di...
 5.5.14: In 1120, use the Remainder Theorem to find the remainder when is di...
 5.5.15: In 1120, use the Remainder Theorem to find the remainder when is di...
 5.5.16: In 1120, use the Remainder Theorem to find the remainder when is di...
 5.5.17: In 1120, use the Remainder Theorem to find the remainder when is di...
 5.5.18: In 1120, use the Remainder Theorem to find the remainder when is di...
 5.5.19: In 1120, use the Remainder Theorem to find the remainder when is di...
 5.5.20: In 1120, use the Remainder Theorem to find the remainder when is di...
 5.5.21: In 2132, tell the maximum number of real zeros that each polynomial...
 5.5.22: In 2132, tell the maximum number of real zeros that each polynomial...
 5.5.23: In 2132, tell the maximum number of real zeros that each polynomial...
 5.5.24: In 2132, tell the maximum number of real zeros that each polynomial...
 5.5.25: In 2132, tell the maximum number of real zeros that each polynomial...
 5.5.26: In 2132, tell the maximum number of real zeros that each polynomial...
 5.5.27: In 2132, tell the maximum number of real zeros that each polynomial...
 5.5.28: In 2132, tell the maximum number of real zeros that each polynomial...
 5.5.29: In 2132, tell the maximum number of real zeros that each polynomial...
 5.5.30: In 2132, tell the maximum number of real zeros that each polynomial...
 5.5.31: In 2132, tell the maximum number of real zeros that each polynomial...
 5.5.32: In 2132, tell the maximum number of real zeros that each polynomial...
 5.5.33: In 3344, list the potential rational zeros of each polynomial funct...
 5.5.34: In 3344, list the potential rational zeros of each polynomial funct...
 5.5.35: In 3344, list the potential rational zeros of each polynomial funct...
 5.5.36: In 3344, list the potential rational zeros of each polynomial funct...
 5.5.37: In 3344, list the potential rational zeros of each polynomial funct...
 5.5.38: In 3344, list the potential rational zeros of each polynomial funct...
 5.5.39: In 3344, list the potential rational zeros of each polynomial funct...
 5.5.40: In 3344, list the potential rational zeros of each polynomial funct...
 5.5.41: In 3344, list the potential rational zeros of each polynomial funct...
 5.5.42: In 3344, list the potential rational zeros of each polynomial funct...
 5.5.43: In 3344, list the potential rational zeros of each polynomial funct...
 5.5.44: In 3344, list the potential rational zeros of each polynomial funct...
 5.5.45: In 4556, use the Rational Zeros Theorem to find all the real zeros ...
 5.5.46: In 4556, use the Rational Zeros Theorem to find all the real zeros ...
 5.5.47: In 4556, use the Rational Zeros Theorem to find all the real zeros ...
 5.5.48: In 4556, use the Rational Zeros Theorem to find all the real zeros ...
 5.5.49: In 4556, use the Rational Zeros Theorem to find all the real zeros ...
 5.5.50: In 4556, use the Rational Zeros Theorem to find all the real zeros ...
 5.5.51: In 4556, use the Rational Zeros Theorem to find all the real zeros ...
 5.5.52: In 4556, use the Rational Zeros Theorem to find all the real zeros ...
 5.5.53: In 4556, use the Rational Zeros Theorem to find all the real zeros ...
 5.5.54: In 4556, use the Rational Zeros Theorem to find all the real zeros ...
 5.5.55: In 4556, use the Rational Zeros Theorem to find all the real zeros ...
 5.5.56: In 4556, use the Rational Zeros Theorem to find all the real zeros ...
 5.5.57: In 5768,solve each equation in the real number system x4  x3 + 2x2...
 5.5.58: In 5768,solve each equation in the real number system 2x3 + 3x2 + 2...
 5.5.59: In 5768,solve each equation in the real number system 3x3 + 4x2  7...
 5.5.60: In 5768,solve each equation in the real number system 2x3  3x2  3...
 5.5.61: In 5768,solve each equation in the real number system 3x3  x2  15...
 5.5.62: In 5768,solve each equation in the real number system 2x3  11x2 + ...
 5.5.63: In 5768,solve each equation in the real number system x4 + 4x3 + 2x...
 5.5.64: In 5768,solve each equation in the real number system x4  2x3 + 10...
 5.5.65: In 5768,solve each equation in the real number system x3  23x2 +83...
 5.5.66: In 5768,solve each equation in the real number system x3 +32x2 + 3x...
 5.5.67: In 5768,solve each equation in the real number system 2x4  19x3 + ...
 5.5.68: In 5768,solve each equation in the real number system 2x4 + x3  24...
 5.5.69: In 6976, find bounds on the real zeros of each polynomial function....
 5.5.70: In 6976, find bounds on the real zeros of each polynomial function....
 5.5.71: In 6976, find bounds on the real zeros of each polynomial function....
 5.5.72: In 6976, find bounds on the real zeros of each polynomial function....
 5.5.73: In 6976, find bounds on the real zeros of each polynomial function....
 5.5.74: In 6976, find bounds on the real zeros of each polynomial function....
 5.5.75: In 6976, find bounds on the real zeros of each polynomial function....
 5.5.76: In 6976, find bounds on the real zeros of each polynomial function....
 5.5.77: In 7782, use the Intermediate Value Theorem to show that each polyn...
 5.5.78: In 7782, use the Intermediate Value Theorem to show that each polyn...
 5.5.79: In 7782, use the Intermediate Value Theorem to show that each polyn...
 5.5.80: In 7782, use the Intermediate Value Theorem to show that each polyn...
 5.5.81: In 7782, use the Intermediate Value Theorem to show that each polyn...
 5.5.82: In 7782, use the Intermediate Value Theorem to show that each polyn...
 5.5.83: In 8386, each equation has a solution r in the interval indicated. ...
 5.5.84: In 8386, each equation has a solution r in the interval indicated. ...
 5.5.85: In 8386, each equation has a solution r in the interval indicated. ...
 5.5.86: In 8386, each equation has a solution r in the interval indicated. ...
 5.5.87: In 8790, each polynomial function has exactly one positive zero. Us...
 5.5.88: In 8790, each polynomial function has exactly one positive zero. Us...
 5.5.89: In 8790, each polynomial function has exactly one positive zero. Us...
 5.5.90: In 8790, each polynomial function has exactly one positive zero. Us...
 5.5.91: In 91102, graph each polynomial function. f1x2 = x3 + 2x2  5x  6
 5.5.92: In 91102, graph each polynomial function. f1x2 = x3 + 8x2 + 11x  20
 5.5.93: In 91102, graph each polynomial function. f1x2 = 2x3  x2 + 2x  1
 5.5.94: In 91102, graph each polynomial function. f1x2 = 2x3 + x2 + 2x + 1
 5.5.95: In 91102, graph each polynomial function. f1x2 = x4 + x2  2
 5.5.96: In 91102, graph each polynomial function. f1x2 = x4  3x2  4
 5.5.97: In 91102, graph each polynomial function. f1x2 = 4x4 + 7x2  2
 5.5.98: In 91102, graph each polynomial function. f1x2 = 4x4 + 15x2  4
 5.5.99: In 91102, graph each polynomial function. f1x2 = x4 + x3  3x2  x + 2
 5.5.100: In 91102, graph each polynomial function. f1x2 = x4  x3  6x2 + 4x...
 5.5.101: In 91102, graph each polynomial function. f1x2 = 4x5  8x4  x + 2
 5.5.102: In 91102, graph each polynomial function. f1x2 = 4x5 + 12x4  x  3
 5.5.103: Find k such that f1x2 = x3  kx2 + kx + 2 has the factor
 5.5.104: Find k such that f1x2 = x4  kx3 + kx2 + 1 has the factor x + 2.
 5.5.105: What is the remainder when f1x2 = 2x20  8x10 + x  2 is divided by ?
 5.5.106: What is the remainder when f1x2 = 3x17 + x9  x5 + 2x is divided b...
 5.5.107: Use the Factor Theorem to prove that is a factor of for any positiv...
 5.5.108: Use the Factor Theorem to prove that is a factor of if is an odd in...
 5.5.109: One solution of the equation x3  8x2 + 16x  3 = 0 is 3. Find the ...
 5.5.110: One solution of the equation x3 + 5x2 + 5x  2 = 0 is . Find the su...
 5.5.111: Geometry What is the length of the edge of a cube if, after a slice...
 5.5.112: Geometry What is the length of the edge of a cube if its volume cou...
 5.5.113: Let be a polynomial function whose coefficients are integers. Suppo...
 5.5.114: Prove the Rational Zeros Theorem. [Hint: Let , where p and q have n...
 5.5.115: Bisection Method for Approximating Zeros of a Function f We begin w...
 5.5.116: Is 1/3 a zero of f1x2 = 2x3 + 3x2  6x + 7? Explain.
 5.5.117: Is 1/3 a zero of f1x2 = 4x 3  5x2  3x + 1? Explain.
 5.5.118: Is a zero of f1x2 = 2x6  5x4 + x3  x + 1 ? Explain.
 5.5.119: Is a zero of f1x2 = x 7 + 6x5  x4 + x + 2? Explain.
Solutions for Chapter 5.5: Algebra and Trigonometry 9th Edition
Full solutions for Algebra and Trigonometry  9th Edition
ISBN: 9780321716569
Solutions for Chapter 5.5
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 119 problems in chapter 5.5 have been answered, more than 61829 students have viewed full stepbystep solutions from this chapter. Algebra and Trigonometry was written by and is associated to the ISBN: 9780321716569. Chapter 5.5 includes 119 full stepbystep solutions. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 9.

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).

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

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

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 column rank r = n.
Independent columns, N(A) = {O}, no free variables.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

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

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

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

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.

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

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).

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).