 A.3.1: The polynomial 3x4  2x3 + 13x2  5 is of degree . The leading coef...
 A.3.2: 1x2  42 1x2 + 42 =
 A.3.3: 1x  22 1x2 + 2x + 42 = .
 A.3.4: 4x2 is a monomial of degree 2.
 A.3.5: 1x + a2 1x2 + ax + a2 = x3 + a3 .
 A.3.6: To check division, the expression that is being divided, the divide...
 A.3.7: If factored completely, 3x3  12x = .
 A.3.8: To complete the square of the expression x2 + 5x, you would the num...
 A.3.9: The polynomial x2 + 4 is prime.
 A.3.10: 3x3  2x2  6x + 4 = 13x  22 1x2 + 22.
 A.3.11: In 1120, tell whether the expression is a monomial. If it is, name ...
 A.3.12: In 1120, tell whether the expression is a monomial. If it is, name ...
 A.3.13: In 1120, tell whether the expression is a monomial. If it is, name ...
 A.3.14: In 1120, tell whether the expression is a monomial. If it is, name ...
 A.3.15: In 1120, tell whether the expression is a monomial. If it is, name ...
 A.3.16: In 1120, tell whether the expression is a monomial. If it is, name ...
 A.3.17: In 1120, tell whether the expression is a monomial. If it is, name ...
 A.3.18: In 1120, tell whether the expression is a monomial. If it is, name ...
 A.3.19: In 1120, tell whether the expression is a monomial. If it is, name ...
 A.3.20: In 1120, tell whether the expression is a monomial. If it is, name ...
 A.3.21: In 2130, tell whether the expression is a polynomial. If it is, giv...
 A.3.22: In 2130, tell whether the expression is a polynomial. If it is, giv...
 A.3.23: In 2130, tell whether the expression is a polynomial. If it is, giv...
 A.3.24: In 2130, tell whether the expression is a polynomial. If it is, giv...
 A.3.25: In 2130, tell whether the expression is a polynomial. If it is, giv...
 A.3.26: In 2130, tell whether the expression is a polynomial. If it is, giv...
 A.3.27: In 2130, tell whether the expression is a polynomial. If it is, giv...
 A.3.28: In 2130, tell whether the expression is a polynomial. If it is, giv...
 A.3.29: In 2130, tell whether the expression is a polynomial. If it is, giv...
 A.3.30: In 2130, tell whether the expression is a polynomial. If it is, giv...
 A.3.31: In 3156, add, subtract, or multiply, as indicated. Express your ans...
 A.3.32: In 3156, add, subtract, or multiply, as indicated. Express your ans...
 A.3.33: In 3156, add, subtract, or multiply, as indicated. Express your ans...
 A.3.34: In 3156, add, subtract, or multiply, as indicated. Express your ans...
 A.3.35: In 3156, add, subtract, or multiply, as indicated. Express your ans...
 A.3.36: In 3156, add, subtract, or multiply, as indicated. Express your ans...
 A.3.37: In 3156, add, subtract, or multiply, as indicated. Express your ans...
 A.3.38: In 3156, add, subtract, or multiply, as indicated. Express your ans...
 A.3.39: In 3156, add, subtract, or multiply, as indicated. Express your ans...
 A.3.40: In 3156, add, subtract, or multiply, as indicated. Express your ans...
 A.3.41: In 3156, add, subtract, or multiply, as indicated. Express your ans...
 A.3.42: In 3156, add, subtract, or multiply, as indicated. Express your ans...
 A.3.43: In 3156, add, subtract, or multiply, as indicated. Express your ans...
 A.3.44: In 3156, add, subtract, or multiply, as indicated. Express your ans...
 A.3.45: In 3156, add, subtract, or multiply, as indicated. Express your ans...
 A.3.46: In 3156, add, subtract, or multiply, as indicated. Express your ans...
 A.3.47: In 3156, add, subtract, or multiply, as indicated. Express your ans...
 A.3.48: In 3156, add, subtract, or multiply, as indicated. Express your ans...
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 A.3.50: In 3156, add, subtract, or multiply, as indicated. Express your ans...
 A.3.51: In 3156, add, subtract, or multiply, as indicated. Express your ans...
 A.3.52: In 3156, add, subtract, or multiply, as indicated. Express your ans...
 A.3.53: In 3156, add, subtract, or multiply, as indicated. Express your ans...
 A.3.54: In 3156, add, subtract, or multiply, as indicated. Express your ans...
 A.3.55: In 3156, add, subtract, or multiply, as indicated. Express your ans...
 A.3.56: In 3156, add, subtract, or multiply, as indicated. Express your ans...
 A.3.57: In 5772, find the quotient and the remainder. Check your work by ve...
 A.3.58: In 5772, find the quotient and the remainder. Check your work by ve...
 A.3.59: In 5772, find the quotient and the remainder. Check your work by ve...
 A.3.60: In 5772, find the quotient and the remainder. Check your work by ve...
 A.3.61: In 5772, find the quotient and the remainder. Check your work by ve...
 A.3.62: In 5772, find the quotient and the remainder. Check your work by ve...
 A.3.63: In 5772, find the quotient and the remainder. Check your work by ve...
 A.3.64: In 5772, find the quotient and the remainder. Check your work by ve...
 A.3.65: In 5772, find the quotient and the remainder. Check your work by ve...
 A.3.66: In 5772, find the quotient and the remainder. Check your work by ve...
 A.3.67: In 5772, find the quotient and the remainder. Check your work by ve...
 A.3.68: In 5772, find the quotient and the remainder. Check your work by ve...
 A.3.69: In 5772, find the quotient and the remainder. Check your work by ve...
 A.3.70: In 5772, find the quotient and the remainder. Check your work by ve...
 A.3.71: In 5772, find the quotient and the remainder. Check your work by ve...
 A.3.72: In 5772, find the quotient and the remainder. Check your work by ve...
 A.3.73: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.74: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.75: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.76: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.77: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.78: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.79: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.80: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.81: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.82: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.83: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.84: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.85: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.86: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.87: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.88: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.89: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.90: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.91: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.92: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.93: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.94: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.95: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.96: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.97: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.98: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.99: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.100: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.101: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.102: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.103: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.104: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.105: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.106: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.107: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.108: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.109: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.110: In 73120, factor completely each polynomial. If the polynomial cann...
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 A.3.118: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.119: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.120: In 73120, factor completely each polynomial. If the polynomial cann...
 A.3.121: In 121126, determine the number that should be added to complete th...
 A.3.122: In 121126, determine the number that should be added to complete th...
 A.3.123: In 121126, determine the number that should be added to complete th...
 A.3.124: In 121126, determine the number that should be added to complete th...
 A.3.125: In 121126, determine the number that should be added to complete th...
 A.3.126: In 121126, determine the number that should be added to complete th...
 A.3.127: In 127136, expressions that occur in calculus are given. Factor com...
 A.3.128: In 127136, expressions that occur in calculus are given. Factor com...
 A.3.129: In 127136, expressions that occur in calculus are given. Factor com...
 A.3.130: In 127136, expressions that occur in calculus are given. Factor com...
 A.3.131: In 127136, expressions that occur in calculus are given. Factor com...
 A.3.132: In 127136, expressions that occur in calculus are given. Factor com...
 A.3.133: In 127136, expressions that occur in calculus are given. Factor com...
 A.3.134: In 127136, expressions that occur in calculus are given. Factor com...
 A.3.135: In 127136, expressions that occur in calculus are given. Factor com...
 A.3.136: In 127136, expressions that occur in calculus are given. Factor com...
 A.3.137: Show that x2 + 4 is prime.
 A.3.138: Show that x2 + x + 1 is prime.
 A.3.139: Explain why the degree of the product of two nonzero polynomials eq...
 A.3.140: Explain why the degree of the sum of two polynomials of different d...
 A.3.141: Give a careful statement about the degree of the sum of two polynom...
 A.3.142: Do you prefer to memorize the rule for the square of a binomial 1x ...
 A.3.143: Make up a polynomial that factors into a perfect square.
 A.3.144: Explain to a fellow student what you look for first when presented ...
Solutions for Chapter A.3: Polynomials
Full solutions for Precalculus Enhanced with Graphing Utilities  6th Edition
ISBN: 9780132854351
Solutions for Chapter A.3: Polynomials
Get Full SolutionsPrecalculus Enhanced with Graphing Utilities was written by and is associated to the ISBN: 9780132854351. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Precalculus Enhanced with Graphing Utilities, edition: 6. Chapter A.3: Polynomials includes 144 full stepbystep solutions. Since 144 problems in chapter A.3: Polynomials have been answered, more than 59630 students have viewed full stepbystep solutions from this chapter.

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

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.

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

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.

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

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

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

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.

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

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).

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

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.

Norm
IIA II. The ".e 2 norm" of A is the maximum ratio II Ax II/l1x II = O"max· Then II Ax II < IIAllllxll and IIABII < IIAIIIIBII and IIA + BII < IIAII + IIBII. Frobenius norm IIAII} = L La~. The.e 1 and.e oo norms are largest column and row sums of laij I.

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).

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

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.