Explanation Given Information: The provided polynomial is 6 x 2 − 19 x − 5 . 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, 6 x 2 − 19 x − 5 Take the combination of two terms, whose product is 6 x 2 , Combination of terms Product 2 x and 3 x 6 x 2 6 x and x 6 x 2 Write this combination in factor form, as, ( 2 x + ) ( 3 x + ) Or ( 6 x + ) ( x + ) Take the possible pairs of two terms, whose product is − 5 , Possible pairs Product of pairs 1 , − 5 − 5 − 1 , 5 − 5 5 , − 1 − 5 − 5 , 1 − 5 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 ( 2 x + 1 ) ( 3 x − 5 ) 6 x 2 − 10 x + 3 x − 5 = 6 x 2 − 7 x − 5 Middle term is not − 19 , So, rejected. ( 2 x − 1 ) ( 3 x + 5 ) 6 x 2 + 10 x − 3 x − 5 = 6 x 2 + 7 x − 5 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 65ES

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To calculate: The factorization of the polynomial 6x2−19x−5.

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Chapter 11.3, Problem 64ES

Chapter 11.3, Problem 66ES

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Chapter 11 Solutions

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The factorization of the polynomial 6 x 2 − 19 x − 5 .

Solution Summary: The author explains how to calculate the factorization of the polynomial 6x2-19x-5 by foil method.

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To calculate: The factorization of the polynomial 6x2−19x−5.

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Chapter 11 Solutions