Explanation Procedure used: Factoring general trinomials by grouping : In a trinomial of the form a x 2 + b x + c , a ≠ 1 , split up the x -term into two terms using the method described below. “Step 1: Find the product a c . Step 2: Find two numbers whose product is a c and whose sums is b . Step 3: Replace the middle term bx with two x -terms having these numbers as coefficients. That is, a x 2 + b x + c = a x 2 + m x + n x + c . Step 4: Complete the factorization by grouping”. Calculation: Factor the given expression x 2 + x − 42 as follows. It is observed that, the coefficients are a = 1 , b = 1 and c = − 42 . Step 1: Find the value of a c . Obtain the value of a c as, a c = 1 ( − 42 ) = − 42 Thus, the value of a c is –42. Step 2: Find the two number, e and f, whose product is a c = − 42 and whose sum is b = 1 . Obtain the list of integer factors of –42 such that product is –42 and sum is 1 as shown below in Table 1. Integers whose product is –42 1 , − 42 − 1 , 42 − 6 , 7 6 , − 7 Sum –41 41 1 –1 Table 1 From Table 1, it is observed that the numbers whose product is –42 and sum is 1 are − 6 and 7 . Let, the integers take the variables e = − 6 and f = 7

Mylab Math With Pearson Etext -- 18 Week Standalone Access Card -- For Basic Technical Mathematics With Calculus

11th Edition

ISBN: 9780135902912

Author: Allyn J. Washington

Publisher: PEARSON

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Chapter 6, Problem 27RE

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Mylab Math With Pearson Etext -- 18 Week Standalone Access Card -- For Basic Technical Mathematics With Calculus

Ch. 6.1 - Prob. 1PE Ch. 6.1 - Prob. 2PE Ch. 6.1 - Prob. 3PE Ch. 6.1 - Prob. 4PE Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E

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To factor: The expression x 2 + x − 42 completely.

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