Explanation Given Information: The provided polynomial is 15 x 2 − 19 x − 10 . Formula used: Follow the steps as mentioned below to compute the factorization of a polynomial a x 2 + b x + c when a ≠ 1 by foil method. Step 1: Take the largest common factor as common, if possible. Step 2: Find the two first terms in a combination whose product will give a x 2 which will represent “ F” in the FOIL. Step 3: Find the two last terms in a combination whose product will give c which will represent “ L” in the FOIL. Step 4: Take the outer product by multiplying first and the last term obtained from step 2 and 3 also take the inner product by multiplying reaming inner terms obtained from step 2 and 3 then take the sum of results to get the value of b x which will represent “OI” in the FOIL. Step 5: Check the result by multiplication. Calculation: Consider the provided polynomial, 15 x 2 − 19 x − 10 Take the combination of two terms, whose product is 15 x 2 , Combination of terms Product 3 x and 5 x 15 x 2 15 x and x 15 x 2 Write this combination in factor form, as, ( 3 x + ) ( 5 x + ) or ( 15 x + ) ( x + ) Take the possible pairs of two terms, whose product is − 10 , Possible pairs Product of pairs 2 , − 5 − 10 − 2 , 5 − 10 5 , − 2 − 10 − 5 , 2 − 10 10 , − 1 − 10 − 10 , 1 − 10 Form the pair to get middle term − 19 by checking each possible pair via substituting the combination in the factor form, as, Trial Product Remark ( 3 x + 2 ) ( 5 x − 5 ) 15 x 2 − 15 x + 10 x − 10 = 15 x 2 − 5 x − 10 Middle term is not − 19 , So, rejected. ( 3 x − 2 ) ( 5 x + 5 ) 15 x 2 + 15 x − 10 x − 10 = 15 x 2 + 5 x − 10 Middle term is not − 19 , So, rejected

9th Edition

ISBN: 9780321997173

Author: Marvin L. Bittinger, Judith A. Beecher

Publisher: PEARSON

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Chapter 11.3, Problem 12ES

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Chapter 11.3, Problem 11ES

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The factorization of the polynomial 15 x 2 − 19 x − 10 .

Solution Summary: The author calculates the factorization of the polynomial 15x2-19x-10 by foil method.

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Chapter 11 Solutions