Explanation Procedure used: To factor the given trinomial by grouping. 1. Check whether the terms are in descending powers of x and verify that the first term is positive. If not multiply with − 1 as the common factor. 2. Find the product of the coefficients of the first term and the last term of the polynomial. 3. Product is factored into a pair of factors whose sum is the coefficient of middle term. (a) If the last term is positive then, the factors will have like sign either both positive or both negative and it depends on the sign of the middle term. (b) If the last term is negative the factors will have unlike signs and it matches the sign of middle term depending on the sign of the largest factor. If none of the factor pair meets the above cases, then the trinomial is prime. 4. The trinomial is now rewritten with a polynomial of four terms such that the middle term is replaced with two terms which are the above identified factors. 5. The polynomial is further grouped into two groups 6. Common factors from each of the two groups are factored. 7. Now the common binomial factor is factored as well. Calculation: The given trinomial is 18 x 2 − 3 x − 10 . Observe that the terms are in descending order and the first term is positive. The product of first and last term is 18 ⋅ ( − 10 ) = − 180 . Find all the factor pairs of 180. 180 = 1 ⋅ 180 = 2.90 = 3 ⋅ 60 = 4 ⋅ 45 The factor pairs can be further extended as follows: 180 = 5 ⋅ 36 = 6.30 = 9.20 = 10 ⋅ 18 = 12.15 The pair whose sum gives − 3 is identified. They are ( − 15 and 12 ) which are both unlike since the last term is negative. In the given trinomial expression ( − 3 x ) is separated into ( − 15 x and1 2 x ) and are grouped and factored out as follows: 18 x 2 − 3 x − 10 = 18 x 2 − 15 x + 12 x − 10 = 3 x ( 6 x − 5 ) + 2 ( 6 x − 5 ) = ( 3 x + 2 ) ( 6 x − 5 ) Check using the FOIL method: x

MML F/COLLEGE MAT F/TRADES - ACCESS CODE

10th Edition

ISBN: 9781323845967

Author: Hobbs

Publisher: PEARSON

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Chapter 13.3, Problem 81E

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To factor: The given trinomial expression by grouping.

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Chapter 13.3, Problem 80E

Chapter 13.3, Problem 82E

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Chapter 13 Solutions

MML F/COLLEGE MAT F/TRADES - ACCESS CODE

Ch. 13.1 - Are 4a and 3a3 like terms? Ch. 13.1 - Name any factor that 4a and 3a3 have in common. Ch. 13.1 - Prob. 1E Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E Ch. 13.1 - Prob. 5E Ch. 13.1 - Prob. 6E Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E

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