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 x 2 − 24 x + 18 as follows. Rewrite the expression 8 x 2 − 24 x + 18 is, 8 x 2 − 24 x + 18 = 2 ( 4 x 2 − 12 x + 9 ) (1) Consider the expression 4 x 2 − 12 x + 9 . It is observed that, the coefficients are a = 4 , b = − 12 and c = 9 . Step 1: Find the value of a c . Obtain the value of a c as, a c = 4 ( 9 ) = 36 Thus, the value of a c is 36. Step 2: Find the two number, m and n, whose product is a c = 36 and whose sum is b = − 12 . Obtain the list of integer factors of 36 such that product is 36 and sum is –12 as shown below in Table 1. Integers whose product is 36 1 , 36 − 36 , − 1 − 9 , − 4 9 , 4 − 6 , − 6 6 , 6 Sum 37 –37 –13 13 –12 12 Table 1 From Table 1, it is observed that the numbers whose product is 36 and sum is –12 are − 6 and − 6 . Let, the variables m = − 6 and n = − 6 . Step 3: Write a x 2 + b x + c = a x 2 + m x + n x + c

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Author: Allyn Washington, Richard Evans

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Chapter 6.2, Problem 37E

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To factor: The given expression 8x2−24x+18 completely.

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Chapter 6.2, Problem 36E

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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 8 x 2 − 24 x + 18 completely.

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Chapter 6 Solutions