 P.4.1: In Exercises 13, fill in the blanks.The process of writing a polyno...
 P.4.2: In Exercises 13, fill in the blanks.A polynomial is ________ ______...
 P.4.3: In Exercises 13, fill in the blanks.If a polynomial has more than t...
 P.4.4: Match the factored form of the polynomial with its name.(a) u2 v2 u...
 P.4.5: In Exercises 58, find the greatest common factor of theexpressions....
 P.4.6: In Exercises 58, find the greatest common factor of theexpressions....
 P.4.7: In Exercises 58, find the greatest common factor of theexpressions....
 P.4.8: In Exercises 58, find the greatest common factor of theexpressions....
 P.4.9: In Exercises 916, factor out the common factor.4x + 16
 P.4.10: In Exercises 916, factor out the common factor.5y  30
 P.4.11: In Exercises 916, factor out the common factor.2x3  6x
 P.4.12: In Exercises 916, factor out the common factor.3z3 = 6z2 + 9z
 P.4.13: In Exercises 916, factor out the common factor.3x x  5 + 8 x 5
 P.4.14: In Exercises 916, factor out the common factor.3x x + 2  4x + 2
 P.4.15: In Exercises 916, factor out the common factor.x + 32  4x + 3
 P.4.16: In Exercises 916, factor out the common factor.5x 4 2 + 5x  4
 P.4.17: In Exercises 1722, find the greatest common factor such thatthe rem...
 P.4.18: In Exercises 1722, find the greatest common factor such thatthe rem...
 P.4.19: In Exercises 1722, find the greatest common factor such thatthe rem...
 P.4.20: In Exercises 1722, find the greatest common factor such thatthe rem...
 P.4.21: In Exercises 1722, find the greatest common factor such thatthe rem...
 P.4.22: In Exercises 1722, find the greatest common factor such thatthe rem...
 P.4.23: In Exercises 2332, completely factor the difference of twosquares.x...
 P.4.24: In Exercises 2332, completely factor the difference of twosquares.x...
 P.4.25: In Exercises 2332, completely factor the difference of twosquares.4...
 P.4.26: In Exercises 2332, completely factor the difference of twosquares.5...
 P.4.27: In Exercises 2332, completely factor the difference of twosquares.1...
 P.4.28: In Exercises 2332, completely factor the difference of twosquares.4...
 P.4.29: In Exercises 2332, completely factor the difference of twosquares.x...
 P.4.30: In Exercises 2332, completely factor the difference of twosquares.2...
 P.4.31: In Exercises 2332, completely factor the difference of twosquares.9...
 P.4.32: In Exercises 2332, completely factor the difference of twosquares.2...
 P.4.33: In Exercises 3344, factor the perfect square trinomial.x2 4x 4
 P.4.34: In Exercises 3344, factor the perfect square trinomial.x2 10x 25
 P.4.35: In Exercises 3344, factor the perfect square trinomial.4t2 4t 1
 P.4.36: In Exercises 3344, factor the perfect square trinomial.9x2 12x 4
 P.4.37: In Exercises 3344, factor the perfect square trinomial.25y2 10y 1
 P.4.38: In Exercises 3344, factor the perfect square trinomial.36y2 108y 81
 P.4.39: In Exercises 3344, factor the perfect square trinomial.9u2 24uv 16v2
 P.4.40: In Exercises 3344, factor the perfect square trinomial.4x2 4xy y2
 P.4.41: In Exercises 3344, factor the perfect square trinomial.x2 43x 49
 P.4.42: In Exercises 3344, factor the perfect square trinomial.z 2 z 14
 P.4.43: In Exercises 3344, factor the perfect square trinomial.4x2 43x 19
 P.4.44: In Exercises 3344, factor the perfect square trinomial.9y2 32 y 1 16
 P.4.45: In Exercises 4556, factor the sum or difference of cubes.x 3 8
 P.4.46: In Exercises 4556, factor the sum or difference of cubes.27 x 3
 P.4.47: In Exercises 4556, factor the sum or difference of cubes.y3 64
 P.4.48: In Exercises 4556, factor the sum or difference of cubes.z3 216
 P.4.49: In Exercises 4556, factor the sum or difference of cubes.x3 827
 P.4.50: In Exercises 4556, factor the sum or difference of cubes.y3 8125
 P.4.51: In Exercises 4556, factor the sum or difference of cubes.8t 3 1
 P.4.52: In Exercises 4556, factor the sum or difference of cubes.273 8
 P.4.53: In Exercises 4556, factor the sum or difference of cubes.u3 27v3
 P.4.54: In Exercises 4556, factor the sum or difference of cubes.64x3 y3
 P.4.55: In Exercises 4556, factor the sum or difference of cubes.x 23 y3
 P.4.56: In Exercises 4556, factor the sum or difference of cubes.x 3y3 8z3
 P.4.57: In Exercises 5770, factor the trinomial.x2 x 2
 P.4.58: In Exercises 5770, factor the trinomial.x2 5x 6
 P.4.59: In Exercises 5770, factor the trinomial.s2 5s 6
 P.4.60: In Exercises 5770, factor the trinomial.t2 t 6
 P.4.61: In Exercises 5770, factor the trinomial.20 y y 2
 P.4.62: In Exercises 5770, factor the trinomial.24 5z z 2
 P.4.63: In Exercises 5770, factor the trinomial.x2 30x 200
 P.4.64: In Exercises 5770, factor the trinomial.x2 13x 42
 P.4.65: In Exercises 5770, factor the trinomial.3x2 5x 2
 P.4.66: In Exercises 5770, factor the trinomial.2x2 x 1
 P.4.67: In Exercises 5770, factor the trinomial.5x2 26x 5
 P.4.68: In Exercises 5770, factor the trinomial.12x2 7x 1
 P.4.69: In Exercises 5770, factor the trinomial.9x2 3z 2
 P.4.70: In Exercises 5770, factor the trinomial.5u2 13u 6
 P.4.71: In Exercises 7178, factor by grouping.x3 x 2 2x 2
 P.4.72: In Exercises 7178, factor by grouping.x3 5x x 2 5x 25
 P.4.73: In Exercises 7178, factor by grouping.2x3 x 2 6x 3
 P.4.74: In Exercises 7178, factor by grouping.5x 3 10x 2 3x 6
 P.4.75: In Exercises 7178, factor by grouping.6 2x 3x 3 x4
 P.4.76: In Exercises 7178, factor by grouping.x 5 2x 3 x 2 2
 P.4.77: In Exercises 7178, factor by grouping.6x3 2x 3x 2 1
 P.4.78: In Exercises 7178, factor by grouping.8x5 6x2 12x3 9
 P.4.79: In Exercises 7984, factor the trinomial by grouping.3x2 10x 8
 P.4.80: In Exercises 7984, factor the trinomial by grouping.2x2 9x 9
 P.4.81: In Exercises 7984, factor the trinomial by grouping.6x2 x 2
 P.4.82: In Exercises 7984, factor the trinomial by grouping.6x2 x 15
 P.4.83: In Exercises 7984, factor the trinomial by grouping.15x2 11x 2
 P.4.84: In Exercises 7984, factor the trinomial by grouping.12x2 13x 1
 P.4.85: In Exercises 85120, completely factor the expression.6x2 54
 P.4.86: In Exercises 85120, completely factor the expression.12x2 48
 P.4.87: In Exercises 85120, completely factor the expression.x3 x2
 P.4.88: In Exercises 85120, completely factor the expression.x 3 4x 2
 P.4.89: In Exercises 85120, completely factor the expression.x3 16x
 P.4.90: In Exercises 85120, completely factor the expression.x3 9x
 P.4.91: In Exercises 85120, completely factor the expression.x2  2x + 1
 P.4.92: In Exercises 85120, completely factor the expression.16 + 6x  x2
 P.4.93: In Exercises 85120, completely factor the expression.1 4x 4x2
 P.4.94: In Exercises 85120, completely factor the expression.9x2 6x 1
 P.4.95: In Exercises 85120, completely factor the expression.2x2 4x 2x3
 P.4.96: In Exercises 85120, completely factor the expression.13x 6 5x2
 P.4.97: In Exercises 85120, completely factor the expression.181x2 29x 8
 P.4.98: In Exercises 85120, completely factor the expression.18x2 196x 116
 P.4.99: In Exercises 85120, completely factor the expression.3x3 x2 15x 5
 P.4.100: In Exercises 85120, completely factor the expression.5 x 4x3 x3
 P.4.101: In Exercises 85120, completely factor the expression.5 x 5x2 x3
 P.4.102: In Exercises 85120, completely factor the expression.x4 4x3 x2 4x
 P.4.103: In Exercises 85120, completely factor the expression.3u 2u2 6 u3
 P.4.104: In Exercises 85120, completely factor the expression.2x3 x2 8x 4
 P.4.105: In Exercises 85120, completely factor the expression.3x3 x2 27x 9
 P.4.106: In Exercises 85120, completely factor the expression.15 x3 x2 x 5
 P.4.107: In Exercises 85120, completely factor the expression.t 1 2 49
 P.4.108: In Exercises 85120, completely factor the expression.x 2 1 2 4x 2
 P.4.109: In Exercises 85120, completely factor the expression.x 32 8 2 36x 2
 P.4.110: In Exercises 85120, completely factor the expression.2t3 16
 P.4.111: In Exercises 85120, completely factor the expression.5x 3 40
 P.4.112: In Exercises 85120, completely factor the expression.4x2x 1 2x 1 2
 P.4.113: In Exercises 85120, completely factor the expression.53 4x 2 83 4x5x 1
 P.4.114: In Exercises 85120, completely factor the expression.2x 1x 3 2 3x 1...
 P.4.115: In Exercises 85120, completely factor the expression.73x 2 21 x 2 3...
 P.4.116: In Exercises 85120, completely factor the expression.7x2x 2 12x x2 ...
 P.4.117: In Exercises 85120, completely factor the expression.3x 22x 14 x 2 ...
 P.4.118: In Exercises 85120, completely factor the expression.2xx 54 x 24x 5 3
 P.4.119: In Exercises 85120, completely factor the expression.5x6 146x53x 23...
 P.4.120: In Exercises 85120, completely factor the expression.x22 x2 14 x 2 15
 P.4.121: GEOMETRIC MODELING In Exercises 121124, matchthe factoring formula ...
 P.4.122: GEOMETRIC MODELING In Exercises 121124, matchthe factoring formula ...
 P.4.123: GEOMETRIC MODELING In Exercises 121124, matchthe factoring formula ...
 P.4.124: GEOMETRIC MODELING In Exercises 121124, matchthe factoring formula ...
 P.4.125: GEOMETRIC MODELING In Exercises 125128, draw ageometric factoring m...
 P.4.126: GEOMETRIC MODELING In Exercises 125128, draw ageometric factoring m...
 P.4.127: GEOMETRIC MODELING In Exercises 125128, draw ageometric factoring m...
 P.4.128: GEOMETRIC MODELING In Exercises 125128, draw ageometric factoring m...
 P.4.129: GEOMETRY In Exercises 129132, write an expression infactored form f...
 P.4.130: GEOMETRY In Exercises 129132, write an expression infactored form f...
 P.4.131: GEOMETRY In Exercises 129132, write an expression infactored form f...
 P.4.132: GEOMETRY In Exercises 129132, write an expression infactored form f...
 P.4.133: In Exercises 133138, completely factor the expression.x442x 132x 2x...
 P.4.134: In Exercises 133138, completely factor the expression.x33x2 122x x2...
 P.4.135: In Exercises 133138, completely factor the expression.2x 5435x 425 ...
 P.4.136: In Exercises 133138, completely factor the expression.x2 5324x 34 4...
 P.4.137: In Exercises 133138, completely factor the expression.5x 13 3x 155x 12
 P.4.138: In Exercises 133138, completely factor the expression.2x 34 4x 122x 32
 P.4.139: In Exercises 139142, find all values of for which thetrinomial can ...
 P.4.140: In Exercises 139142, find all values of for which thetrinomial can ...
 P.4.141: In Exercises 139142, find all values of for which thetrinomial can ...
 P.4.142: In Exercises 139142, find all values of for which thetrinomial can ...
 P.4.143: In Exercises 143146, find two integer values of such thatthe trinom...
 P.4.144: In Exercises 143146, find two integer values of such thatthe trinom...
 P.4.145: In Exercises 143146, find two integer values of such thatthe trinom...
 P.4.146: In Exercises 143146, find two integer values of such thatthe trinom...
 P.4.147: GEOMETRY The volume of concrete used to makethe cylindrical concret...
 P.4.148: CHEMISTRY The rate of change of an autocatalyticchemical reaction i...
 P.4.149: TRUE OR FALSE? In Exercises 149 and 150, determinewhether the state...
 P.4.150: TRUE OR FALSE? In Exercises 149 and 150, determinewhether the state...
 P.4.151: ERROR ANALYSIS Describe the error.
 P.4.152: THINK ABOUT IT Is 3x 6x 1 completelyfactored? Explain.
 P.4.153: Factor x2n y2n as completely as possible.
 P.4.154: Factor x3n y3n as completely as possible.
 P.4.155: Give an example of a polynomial that is prime withrespect to the in...
 P.4.156: CAPSTONE Explan what is meant when it is saidthat a polynomial is i...
 P.4.157: Rewrite u6 v6 as the difference of two squares. Thenfind a formula ...
Solutions for Chapter P.4: Factoring Polynomials
Full solutions for College Algebra  8th Edition
ISBN: 9781439048696
Solutions for Chapter P.4: Factoring Polynomials
Get Full SolutionsSince 157 problems in chapter P.4: Factoring Polynomials have been answered, more than 36926 students have viewed full stepbystep solutions from this chapter. College Algebra was written by and is associated to the ISBN: 9781439048696. This textbook survival guide was created for the textbook: College Algebra , edition: 8. This expansive textbook survival guide covers the following chapters and their solutions. Chapter P.4: Factoring Polynomials includes 157 full stepbystep solutions.

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).

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

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

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.

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.

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.

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

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

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

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

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

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

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).

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

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Solvable system Ax = b.
The right side b is in the column space of A.

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.