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 2 k 2 − k − 36 as follows. It is observed that, the coefficients are a = 2 , b = − 1 and c = − 36 . Step 1: Find the value of a c . Obtain the value of a c as, a c = 2 ( − 36 ) = − 72 Thus, the value of a c is –72. Step 2: Find the two number, e and f, whose product is a c = − 72 and whose sum is b = − 1 . Obtain the list of integer factors of –72 such that product is –72 and sum is –1 as shown below in Table 1. Integers whose product is –72 1 , − 72 − 1 , 72 − 9 , 8 9 , − 8 Sum –71 71 –1 1 Table 1 From Table 1, it is observed that the numbers whose product is –72 and sum is –1 are − 9 and 8 . Let, the integers take the variables e = − 9 and f = 8

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ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 6, Problem 31RE

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To factor: The expression 2k2−k−36 completely.

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Basic Technical Mathematics

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 2 k 2 − k − 36 completely.

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To factor: The expression 2k2−k−36 completely.

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