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 d 4 − 10 d 2 + 16 as follows. Rewrite the expression as, d 4 − 10 d 2 + 16 = ( d 2 ) 2 − 10 d 2 + 16 . It is observed that, the coefficients are a = 1 , b = − 10 and c = 16 . Step 1: Find the value of a c . Obtain the value of a c as, a c = 1 ( 16 ) = 16 Thus, the value of a c is 16. Step 2: Find the two number, e and f, whose product is a c = 16 and whose sum is b = − 10 . Obtain the list of integer factors of 16 such that product is 16 and sum is –10 as shown below in Table 1. Integers whose product is 16 1 , 16 − 16 , − 1 − 2 , − 8 8 , 2 Sum 17 –17 –10 10 Table 1 From Table 1, it is observed that the numbers whose product is 16 and sum is –10 are − 2 and − 8 . Let the variables e = − 2 and f = − 8 . Step 3: Write a x 2 + b x + c = a x 2 + m x + n x + c

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 6.2, Problem 57E

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To factor: The expression d4−10d2+16 completely.

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Chapter 6.2, Problem 56E

Chapter 6.2, Problem 58E

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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 d 4 − 10 d 2 + 16 completely.

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To factor: The expression d4−10d2+16 completely.

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Chapter 6 Solutions