Explanation Theorem used: a c Test for Factorability. If in polynomials of the form a x 2 + b x + c or a x 2 + b x y + c y 2 , the product a c has the two integer factors p and q whose sum is the coefficient b of the middle term. That is, if the such integers p and q exist so that p q = a c and p + q = b . Then the above polynomials have first-degree factors with integer’s coefficients. If no integer’s p and q exist, then the given polynomials will not have first-degree factors. Theorem 2: Special Factoring Formulas: 1. u 2 + 2 u v + v 2 = ( u + v ) 2 2. u 2 − 2 u v + v 2 = ( u − v ) 2 3. u 2 − v 2 = ( u − v ) ( u + v ) 4. u 3 − v 3 = ( u − v ) ( u 2 + u v + v 2 ) 5

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14th Edition

ISBN: 9780137553341

Author: Raymond Barnett, Michael Ziegler

Publisher: PEARSON+

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Chapter A.3, Problem 55E

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To find: The factors of the polynomial 15y(x−y)3+12x(x−y)2 if not explain the reason.

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Chapter A.3, Problem 54E

Chapter A.3, Problem 56E

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Chapter A Solutions

Pearson eText for College Mathematics for Business, Economics, Life Sciences, and Social Sciences -- Instant Access (Pearson+)

Ch. A.1 - State the real number property that justifies the...Ch. A.1 - Prob. 2MP Ch. A.1 - Prob. 3MP Ch. A.1 - Prob. 1E Ch. A.1 - Prob. 2E Ch. A.1 - Prob. 3E Ch. A.1 - Prob. 4E Ch. A.1 - Prob. 5E Ch. A.1 - Prob. 6E Ch. A.1 - Prob. 7E

Ch. A.1 - Prob. 8E Ch. A.1 - Prob. 9E Ch. A.1 - Prob. 10E Ch. A.1 - Prob. 11E Ch. A.1 - Prob. 12E Ch. A.1 - Prob. 13E Ch. A.1 - Prob. 14E Ch. A.1 - Prob. 15E Ch. A.1 - Prob. 16E Ch. A.1 - Prob. 17E Ch. A.1 - Prob. 18E Ch. A.1 - Prob. 19E Ch. A.1 - Prob. 20E Ch. A.1 - Prob. 21E Ch. A.1 - Prob. 22E Ch. A.1 - Prob. 23E Ch. A.1 - Prob. 24E Ch. A.1 - Prob. 25E Ch. A.1 - Prob. 26E Ch. A.1 - Prob. 27E Ch. A.1 - Prob. 28E Ch. A.1 - Prob. 29E Ch. A.1 - Prob. 30E Ch. A.1 - Prob. 31E Ch. A.1 - Prob. 32E Ch. A.1 - Prob. 33E Ch. A.1 - Prob. 34E Ch. A.1 - Prob. 35E Ch. A.1 - Prob. 36E Ch. A.1 - Prob. 37E Ch. A.1 - Prob. 38E Ch. A.1 - Prob. 39E Ch. A.1 - Prob. 40E Ch. A.1 - Prob. 41E Ch. A.1 - Prob. 42E Ch. A.1 - Prob. 43E Ch. A.1 - Prob. 44E Ch. A.1 - Prob. 45E Ch. A.1 - Prob. 46E Ch. A.1 - Prob. 47E Ch. A.1 - Prob. 48E Ch. A.2 - Prob. 1MP Ch. A.2 - Prob. 2MP Ch. A.2 - Prob. 3MP Ch. A.2 - Prob. 4MP Ch. A.2 - Prob. 5MP Ch. A.2 - Prob. 6MP Ch. A.2 - Perform the indicated operations and...Ch. A.2 - Prob. 1E Ch. A.2 - Prob. 2E Ch. A.2 - Prob. 3E Ch. A.2 - Prob. 4E Ch. A.2 - Prob. 5E Ch. A.2 - Prob. 6E Ch. A.2 - Prob. 7E Ch. A.2 - Prob. 8E Ch. A.2 - Prob. 9E Ch. A.2 - Prob. 10E Ch. A.2 - Prob. 11E Ch. A.2 - Prob. 12E Ch. A.2 - Prob. 13E Ch. A.2 - Prob. 14E Ch. A.2 - Prob. 15E Ch. A.2 - Prob. 16E Ch. A.2 - Prob. 17E Ch. A.2 - Prob. 18E Ch. A.2 - Prob. 19E Ch. A.2 - Prob. 20E Ch. A.2 - Prob. 21E Ch. A.2 - Prob. 22E Ch. A.2 - Prob. 23E Ch. A.2 - Prob. 24E Ch. A.2 - Prob. 25E Ch. A.2 - Prob. 26E Ch. A.2 - Prob. 27E Ch. A.2 - Prob. 28E Ch. A.2 - Prob. 29E Ch. A.2 - Prob. 30E Ch. A.2 - Prob. 31E Ch. A.2 - Prob. 32E Ch. A.2 - Prob. 33E Ch. A.2 - Prob. 34E Ch. A.2 - Prob. 35E Ch. A.2 - Prob. 36E Ch. A.2 - Prob. 37E Ch. A.2 - Prob. 38E Ch. A.2 - Prob. 39E Ch. A.2 - Prob. 40E Ch. A.2 - Prob. 41E Ch. A.2 - Prob. 42E Ch. A.2 - Prob. 43E Ch. A.2 - Prob. 44E Ch. A.2 - 45. Subtract the sum of the last two polynomials...Ch. A.2 - Prob. 46E Ch. A.2 - Prob. 47E Ch. A.2 - Prob. 48E Ch. A.2 - Prob. 49E Ch. A.2 - Prob. 50E Ch. A.2 - Prob. 51E Ch. A.2 - Prob. 52E Ch. A.2 - Prob. 53E Ch. A.2 - Prob. 54E Ch. A.2 - Prob. 55E Ch. A.2 - Prob. 56E Ch. A.2 - Prob. 57E Ch. A.2 - Prob. 58E Ch. A.2 - Prob. 59E Ch. A.2 - Prob. 60E Ch. A.2 - Prob. 61E Ch. A.2 - Prob. 62E Ch. A.3 - Prob. 1MP Ch. A.3 - Prob. 2MP Ch. A.3 - Prob. 3MP Ch. A.3 - Prob. 4MP Ch. A.3 - Prob. 5MP Ch. A.3 - Prob. 1E Ch. A.3 - Prob. 2E Ch. A.3 - Prob. 3E Ch. A.3 - Prob. 4E Ch. A.3 - Prob. 5E Ch. A.3 - Prob. 6E Ch. A.3 - Prob. 7E Ch. A.3 - Prob. 8E Ch. A.3 - Prob. 9E Ch. A.3 - Prob. 10E Ch. A.3 - Prob. 11E Ch. A.3 - Prob. 12E Ch. A.3 - Prob. 13E Ch. A.3 - Prob. 14E Ch. A.3 - Prob. 15E Ch. A.3 - Prob. 16E Ch. A.3 - Prob. 17E Ch. A.3 - Prob. 18E Ch. A.3 - Prob. 19E Ch. A.3 - Prob. 20E Ch. A.3 - In Problems 9–56, factor completely. If a...Ch. A.3 - Prob. 22E Ch. A.3 - Prob. 23E Ch. A.3 - Prob. 24E Ch. A.3 - Prob. 25E Ch. A.3 - Prob. 26E Ch. A.3 - Prob. 27E Ch. A.3 - Prob. 28E Ch. A.3 - Prob. 29E Ch. A.3 - Prob. 30E Ch. A.3 - Prob. 31E Ch. A.3 - Prob. 32E Ch. A.3 - Prob. 33E Ch. A.3 - Prob. 34E Ch. A.3 - Prob. 35E Ch. A.3 - Prob. 36E Ch. A.3 - In Problems 9–56, factor completely. If a...Ch. A.3 - Prob. 38E Ch. A.3 - Prob. 39E Ch. A.3 - Prob. 40E Ch. A.3 - Prob. 41E Ch. A.3 - Prob. 42E Ch. A.3 - Prob. 43E Ch. A.3 - Prob. 44E Ch. A.3 - Prob. 45E Ch. A.3 - Prob. 46E Ch. A.3 - Prob. 47E Ch. A.3 - Prob. 48E Ch. A.3 - Prob. 49E Ch. A.3 - Prob. 50E Ch. A.3 - Prob. 51E Ch. A.3 - Prob. 52E Ch. A.3 - Prob. 53E Ch. A.3 - Prob. 54E Ch. A.3 - Prob. 55E Ch. A.3 - Prob. 56E Ch. A.3 - Prob. 57E Ch. A.3 - Prob. 58E Ch. A.3 - Prob. 59E Ch. A.3 - Prob. 60E Ch. A.4 - Prob. 1MP Ch. A.4 - Prob. 2MP Ch. A.4 - Prob. 3MP Ch. A.4 - Prob. 4MP Ch. A.4 - Prob. 5MP Ch. A.4 - Prob. 1E Ch. A.4 - Prob. 2E Ch. A.4 - Prob. 3E Ch. A.4 - Prob. 4E Ch. A.4 - Prob. 5E Ch. A.4 - Prob. 6E Ch. A.4 - Prob. 7E Ch. A.4 - Prob. 8E Ch. A.4 - Prob. 9E Ch. A.4 - Prob. 10E Ch. A.4 - Prob. 11E Ch. A.4 - Prob. 12E Ch. A.4 - Prob. 13E Ch. A.4 - Prob. 14E Ch. A.4 - Prob. 15E Ch. A.4 - Prob. 16E Ch. A.4 - Prob. 17E Ch. A.4 - Prob. 18E Ch. A.4 - Prob. 19E Ch. A.4 - Prob. 20E Ch. A.4 - Prob. 21E Ch. A.4 - Prob. 22E Ch. A.4 - Prob. 23E Ch. A.4 - Prob. 24E Ch. A.4 - Prob. 25E Ch. A.4 - Prob. 26E Ch. A.4 - Prob. 27E Ch. A.4 - Prob. 28E Ch. A.4 - Prob. 29E Ch. A.4 - Prob. 30E Ch. A.4 - Prob. 31E Ch. A.4 - Prob. 32E Ch. A.4 - Prob. 33E Ch. A.4 - Prob. 34E Ch. A.4 - Prob. 35E Ch. A.4 - Prob. 36E Ch. A.4 - Prob. 37E Ch. A.4 - Prob. 38E Ch. A.4 - Prob. 39E Ch. A.4 - Prob. 40E Ch. A.4 - Prob. 41E Ch. A.4 - Prob. 42E Ch. A.4 - Prob. 43E Ch. A.4 - Prob. 44E Ch. A.4 - Prob. 45E Ch. A.4 - Prob. 46E Ch. A.5 - Prob. 1MP Ch. A.5 - Prob. 2MP Ch. A.5 - Prob. 3MP Ch. A.5 - Prob. 1E Ch. A.5 - Prob. 2E Ch. A.5 - Prob. 3E Ch. A.5 - Prob. 4E Ch. A.5 - Prob. 5E Ch. A.5 - Prob. 6E Ch. A.5 - Prob. 7E Ch. A.5 - Prob. 8E Ch. A.5 - Prob. 9E Ch. A.5 - Prob. 10E Ch. A.5 - Prob. 11E Ch. A.5 - Prob. 12E Ch. A.5 - Prob. 13E Ch. A.5 - Prob. 14E Ch. A.5 - Prob. 15E Ch. A.5 - Prob. 16E Ch. A.5 - Prob. 17E Ch. A.5 - Prob. 18E Ch. A.5 - Prob. 19E Ch. A.5 - In Problems 15–20, write each number in scientific...Ch. A.5 - Prob. 21E Ch. A.5 - Prob. 22E Ch. A.5 - Prob. 23E Ch. A.5 - Prob. 24E Ch. A.5 - Prob. 25E Ch. A.5 - Prob. 26E Ch. A.5 - Prob. 27E Ch. A.5 - In Problems 21–28, write each number in standard...Ch. A.5 - Prob. 29E Ch. A.5 - Prob. 30E Ch. A.5 - Prob. 31E Ch. A.5 - Prob. 32E Ch. A.5 - Prob. 33E Ch. A.5 - Prob. 34E Ch. A.5 - Prob. 35E Ch. A.5 - Prob. 36E Ch. A.5 - Prob. 37E Ch. A.5 - Prob. 38E Ch. A.5 - Prob. 39E Ch. A.5 - Prob. 40E Ch. A.5 - Prob. 41E Ch. A.5 - Prob. 42E Ch. A.5 - Prob. 43E Ch. A.5 - Prob. 44E Ch. A.5 - Prob. 45E Ch. A.5 - Prob. 46E Ch. A.5 - Prob. 47E Ch. A.5 - Prob. 48E Ch. A.5 - Prob. 49E Ch. A.5 - Prob. 50E Ch. A.5 - Prob. 51E Ch. A.5 - Prob. 52E Ch. A.5 - Prob. 53E Ch. A.5 - Prob. 54E Ch. A.5 - Prob. 55E Ch. A.5 - Prob. 56E Ch. A.5 - Prob. 57E Ch. A.5 - Prob. 58E Ch. A.5 - Prob. 59E Ch. A.5 - Prob. 60E Ch. A.5 - Prob. 61E Ch. A.5 - Prob. 62E Ch. A.5 - Prob. 63E Ch. A.5 - Prob. 64E Ch. A.6 - Prob. 1MP Ch. A.6 - Prob. 2MP Ch. A.6 - Prob. 3MP Ch. A.6 - Prob. 4MP Ch. A.6 - Prob. 5MP Ch. A.6 - Prob. 6MP Ch. A.6 - Prob. 7MP Ch. A.6 - Prob. 8MP Ch. A.6 - Prob. 1E Ch. A.6 - Prob. 2E Ch. A.6 - Prob. 3E Ch. A.6 - Prob. 4E Ch. A.6 - Prob. 5E Ch. A.6 - Prob. 6E Ch. A.6 - Prob. 7E Ch. A.6 - Prob. 8E Ch. A.6 - Prob. 9E Ch. A.6 - Prob. 10E Ch. A.6 - Prob. 11E Ch. A.6 - Prob. 12E Ch. A.6 - Prob. 13E Ch. A.6 - Prob. 14E Ch. A.6 - Prob. 15E Ch. A.6 - Prob. 16E Ch. A.6 - Prob. 17E Ch. A.6 - Prob. 18E Ch. A.6 - Prob. 19E Ch. A.6 - Prob. 20E Ch. A.6 - Prob. 21E Ch. A.6 - Prob. 22E Ch. A.6 - Prob. 23E Ch. A.6 - Prob. 24E Ch. A.6 - Prob. 25E Ch. A.6 - Prob. 26E Ch. A.6 - Prob. 27E Ch. A.6 - Prob. 28E Ch. A.6 - Prob. 29E Ch. A.6 - Prob. 30E Ch. A.6 - Prob. 31E Ch. A.6 - Prob. 32E Ch. A.6 - Prob. 33E Ch. A.6 - Prob. 34E Ch. A.6 - Prob. 35E Ch. A.6 - Prob. 36E Ch. A.6 - Prob. 37E Ch. A.6 - Prob. 38E Ch. A.6 - Prob. 39E Ch. A.6 - Prob. 40E Ch. A.6 - Prob. 41E Ch. A.6 - Prob. 42E Ch. A.6 - Prob. 43E Ch. A.6 - Prob. 44E Ch. A.6 - Prob. 45E Ch. A.6 - Prob. 46E Ch. A.6 - Prob. 47E Ch. A.6 - Prob. 48E Ch. A.6 - Prob. 49E Ch. A.6 - Prob. 50E Ch. A.6 - Prob. 51E Ch. A.6 - Prob. 52E Ch. A.6 - Prob. 53E Ch. A.6 - Prob. 54E Ch. A.6 - Prob. 55E Ch. A.6 - Prob. 56E Ch. A.6 - Prob. 57E Ch. A.6 - Prob. 58E Ch. A.6 - Prob. 59E Ch. A.6 - Prob. 60E Ch. A.6 - Prob. 61E Ch. A.6 - Prob. 62E Ch. A.6 - Prob. 63E Ch. A.6 - Prob. 64E Ch. A.6 - Prob. 65E Ch. A.6 - Prob. 66E Ch. A.6 - Prob. 67E Ch. A.6 - Prob. 68E Ch. A.6 - Prob. 69E Ch. A.6 - Prob. 70E Ch. A.6 - Prob. 71E Ch. A.6 - Prob. 72E Ch. A.6 - Prob. 73E Ch. A.6 - Prob. 74E Ch. A.6 - Prob. 75E Ch. A.6 - Prob. 76E Ch. A.6 - Prob. 77E Ch. A.6 - Prob. 78E Ch. A.6 - Prob. 79E Ch. A.6 - Prob. 80E Ch. A.6 - Prob. 81E Ch. A.6 - Prob. 82E Ch. A.6 - Prob. 83E Ch. A.6 - Prob. 84E Ch. A.6 - Prob. 85E Ch. A.6 - Prob. 86E Ch. A.6 - Prob. 87E Ch. A.6 - Prob. 88E Ch. A.6 - Prob. 89E Ch. A.6 - Prob. 90E Ch. A.6 - Prob. 91E Ch. A.6 - Prob. 92E Ch. A.6 - Prob. 93E Ch. A.6 - Prob. 94E Ch. A.6 - Prob. 95E Ch. A.6 - Prob. 96E Ch. A.7 - Prob. 1MP Ch. A.7 - Solve by factoring using integer coefficients, if...Ch. A.7 - Prob. 3MP Ch. A.7 - Prob. 4MP Ch. A.7 - Prob. 5MP Ch. A.7 - Prob. 6MP Ch. A.7 - Prob. 1E Ch. A.7 - Prob. 2E Ch. A.7 - Prob. 3E Ch. A.7 - Prob. 4E Ch. A.7 - Prob. 5E Ch. A.7 - Prob. 6E Ch. A.7 - Prob. 7E Ch. A.7 - Prob. 8E Ch. A.7 - Prob. 9E Ch. A.7 - Prob. 10E Ch. A.7 - Prob. 11E Ch. A.7 - Prob. 12E Ch. A.7 - Prob. 13E Ch. A.7 - Prob. 14E Ch. A.7 - Prob. 15E Ch. A.7 - Prob. 16E Ch. A.7 - Prob. 17E Ch. A.7 - Prob. 18E Ch. A.7 - Prob. 19E Ch. A.7 - Prob. 20E Ch. A.7 - Prob. 21E Ch. A.7 - Prob. 22E Ch. A.7 - Prob. 23E Ch. A.7 - Prob. 24E Ch. A.7 - Prob. 25E Ch. A.7 - Prob. 26E Ch. A.7 - Prob. 27E Ch. A.7 - Prob. 28E Ch. A.7 - Prob. 29E Ch. A.7 - Prob. 30E Ch. A.7 - Prob. 31E Ch. A.7 - Prob. 32E Ch. A.7 - Prob. 33E Ch. A.7 - Prob. 34E Ch. A.7 - Prob. 35E Ch. A.7 - Prob. 36E Ch. A.7 - Prob. 37E Ch. A.7 - Prob. 38E Ch. A.7 - Prob. 39E Ch. A.7 - Prob. 40E Ch. A.7 - Prob. 41E Ch. A.7 - Prob. 42E Ch. A.7 - Prob. 43E Ch. A.7 - Prob. 44E Ch. A.7 - Prob. 45E Ch. A.7 - Prob. 46E Ch. A.7 - Prob. 47E Ch. A.7 - Prob. 48E Ch. A.7 - Prob. 49E Ch. A.7 - Prob. 50E Ch. A.7 - Prob. 51E Ch. A.7 - Prob. 52E Ch. A.7 - Prob. 53E Ch. A.7 - Prob. 54E

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The factors of the polynomial 15 y ( x − y ) 3 + 12 x ( x − y ) 2 if not explain the reason.

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To find: The factors of the polynomial 15y(x−y)3+12x(x−y)2 if not explain the reason.

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Chapter A Solutions