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 8 ( b 3 ) 2 + 31 ( b 3 ) − 4 as follows. It is observed that, the coefficients are a = 8 , b = 31 and c = − 4 . Step 1: Find the value of a c . Obtain the value of a c as, a c = 8 ( − 4 ) = − 32 Thus, the value of a c is –32. Step 2: Find the two number, e and f, whose product is a c = − 32 and whose sum is b = 31 . Obtain the list of integer factors of –32 such that product is –32 and sum is 31 as shown below in Table 1. Integers whose product is –32 1 , − 32 − 1 , 32 − 16 , 2 16 , − 2 Sum –31 31 –14 14 Table 1 From Table 1, it is observed that the numbers whose product is –32 and sum is 31 are − 1 and 32 . Let, the integers take the variables e = − 1 and f = 32 . Step 3: Write a x 2 + b x + c = a x 2 + m x + n x + c . Rewrite the expression 8 ( b 3 ) 2 + 31 ( b 3 ) − 4 in the form a ( b 3 ) 2 + e ( b 3 ) + f ( b 3 ) + c as, 8 ( b 3 ) 2 + 31 ( b 3 ) − 4 = 8 ( b 3 ) 2 − b 3 + 32 b 3 − 4 Step 4: Factor the expression in step 3 by grouping

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

11th Edition

ISBN: 9780134434636

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 6.2, Problem 41E

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To factor: The expression 8b6+31b3−4 completely.

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Chapter 6.2, Problem 40E

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Chapter 6 Solutions

Student Solutions Manual For Basic Technical Mathematics And 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 8 b 6 + 31 b 3 − 4 completely.

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To factor: The expression 8b6+31b3−4 completely.

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Chapter 6 Solutions