Explanation Given Information: The provided polynomial is 30 x 2 − 24 x − 54 . 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 polynomial, 30 x 2 − 24 x − 54 Take out the largest common factor 6 as common, 30 x 2 − 24 x − 54 = 6 ( 5 x 2 − 4 x − 9 ) Now first compute the factors of 5 x 2 − 4 x − 9 , as, Take the combination of two terms, whose product is 5 x 2 , Combination of terms Product 5 x and x 5 x 2 Write this combination in factor form, as, ( 5 x + ) ( x + ) Take the possible pairs of two terms, whose product is − 9 , Possible pairs Product of pairs 3 , − 3 − 9 − 3 , 3 − 9 9 , − 1 − 9 − 9 , 1 − 9 1 , − 9 − 9 − 1 , 9 − 9 Form the pair to get middle term − 4 by checking each possible pair via substituting the combination in the factor form, as, Trial Product Remark ( 5 x + 3 ) ( x − 3 ) 5 x 2 − 15 x + 3 x − 9 = 5 x 2 − 12 x − 9 Middle term is not − 4 , So, this pair is wrong ( 5 x − 3 ) ( x + 3 ) 5 x 2 + 15 x − 3 x − 9 = 5 x 2 + 12 x − 9 Middle term is not − 4 , So, this pair is wrong

9th Edition

ISBN: 9780321997173

Author: Marvin L. Bittinger, Judith A. Beecher

Publisher: PEARSON

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Chapter 11.3, Problem 33ES

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To calculate: The factor of the polynomial 30x2−24x−54.

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Chapter 11.3, Problem 32ES

Chapter 11.3, Problem 34ES

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Chapter 11 Solutions

Developmental Mathematics (9th Edition)

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The factor of the polynomial 30 x 2 − 24 x − 54 .

Solution Summary: The author calculates the factorization of the polynomial ax2+bx+c by foil method.

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To calculate: The factor of the polynomial 30x2−24x−54.

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Chapter 11 Solutions