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 3 − 2 x − 5 x 2 as follows. It is observed that, the coefficients are a = − 5 , b = − 2 and c = 3 . Step 1: Find the value of a c . Obtain the value of a c as, a c = − 5 ( 3 ) = − 15 Thus, the value of a c is –15. Step 2: Find the two number, e and f, whose product is a c = − 15 and whose sum is b = − 2 . Obtain the list of integer factors of –15 such that product is –15 and sum is –2 as shown below in Table 1. Integers whose product is –15 1 , − 15 − 1 , 15 − 3 , 5 3 , − 5 Sum –14 14 2 –2 Table 1 From Table 1, it is observed that the numbers whose product is –15 and sum is –2 are − 5 and 3 . Let, the integers take the variables e = − 5 and f = 3

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

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ISBN: 9780137554843

Author: Allyn Washington, Richard Evans

Publisher: PEARSON+

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Chapter 6, Problem 32RE

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To factor: The expression 3−2x−5x2 completely.

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Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

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 3 − 2 x − 5 x 2 completely.

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To factor: The expression 3−2x−5x2 completely.

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Chapter 6 Solutions