Explanation Given Information: The provided trinomial is, 3 p 2 − 16 p q − 12 q 2 Formula Used: Steps to factorize a trinomial by using a c -method are as follows: Step1. Factor out any common factor other than 1 or − 1 , if possible. Step2. Consider the remaining trinomial in the standard form a p 2 + b p + c , where a ≠ 0 Step3. Factorize the product a c as sum of b or, compute the integers p and q where p q = a c and p + q = b . Step4. Spilt the middle term b as p + q . Step5. Factorize by using grouping. Step6. Verify the product of factors. Calculation: Consider the provided trinomial, 3 p 2 − 16 p q − 12 q 2 Compare the trinomial 3 p 2 − 16 p q − 12 q 2 with the standard form a p 2 + b p + c , where a ≠ 0 , this gives, a = 3 , b = − 16 q and c = − 12 q 2 Compute the product a c , such that sum of the factors equals to b , a c = 3 ⋅ − 12 q 2 = − 36 q 2 Factorize the product − 36 q 2 such that sum of the factors equals to − 16 q . Pairs of factors Sums of factors p , − 36 p − 35 q − p , 36 p 35 q 2 q , − 18 q − 16 − 2 q , 18 q 16 The factors 2 q and − 18 q can be expressed as the sum of coefficient of middle term − 16 q

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ISBN: 9780321997173

Author: Marvin L. Bittinger, Judith A. Beecher

Publisher: PEARSON

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Chapter 11.4, Problem 84ES

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To calculate: The factorization of the trinomial 3p2−16pq−12q2 by using ac-method.

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Chapter 11.4, Problem 83ES

Chapter 11.4, Problem 85ES

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The factorization of the trinomial 3 p 2 − 16 p q − 12 q 2 by using a c -method.

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