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 12 n 4 + 8 n 2 − 15 as follows. Rewrite the expression 12 n 4 + 8 n 2 − 15 as, 12 n 4 + 8 n 2 − 15 = 12 ( n 2 ) 2 + 8 ( n 2 ) − 15 . It is observed that, the coefficients are a = 12 , b = 8 and c = − 15 . Step 1: Find the value of a c . Obtain the value of a c as, a c = 12 ( − 15 ) = − 180 Thus, the value of a c is –180. Step 2: Find the two number, e and f, whose product is a c = − 180 and whose sum is b = 8 . Obtain the list of integer factors of –180 such that product is –180 and sum is 8 as shown below in Table 1. Integers whose product is –180 1 , − 180 180 , − 1 18 , − 10 − 18 , 10 Sum –179 179 8 –8 Table 1 From Table 1, it is observed that the numbers whose product is –180 and sum is 8 are − 10 and 18 . Let, the variables e = − 10 and f = 18 . Step 3: Write a x 2 + b x + c = a x 2 + m x + n x + c

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ISBN: 9780137554843

Author: Allyn Washington, Richard Evans

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Chapter 6.2, Problem 42E

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To factor: The given expression 12n4+8n2−15 completely.

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Chapter 6.2, Problem 41E

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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 given expression 12 n 4 + 8 n 2 − 15 completely.

Solution Summary: The author explains how to factor the given expression 12n4+8. Then, they split up the x-term into two terms.

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To factor: The given expression 12n4+8n2−15 completely.

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Chapter 6 Solutions