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 x 2 + 47 x y − 4 y 2 as follows. Rewrite the expression as, 12 x 2 + 47 x y − 4 y 2 = 12 x 2 + ( 47 y ) x − 4 y 2 . It is observed that, the coefficients are a = 12 , b = 47 y and c = − 4 y 2 . Step 1: Find the value of a c . Obtain the value of a c as, a c = 12 ( − 4 y 2 ) = − 48 y 2 Thus, the value of a c is − 48 y 2 . Step 2: Find the two number, e and f, whose product is a c = − 48 y 2 and whose sum is b = 47 y . Obtain the list of integer factors of − 48 y 2 such that the product is − 48 y 2 and the sum is 47 y as shown below in Table 1. Integers whose product is − 48 y 2 y , − 48 y 12 y , − 4 y − 12 y , 4 y − y , 48 y Sum − 47 y 8 y − 8 y 47 y Table 1 From Table 1, it is observed that the numbers whose product is − 48 y 2 and sum is 47 y are − y and 48 y

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ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 6.2, Problem 45E

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To factor: The expression 12x2+47xy−4y2 completely.

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Chapter 6.2, Problem 44E

Chapter 6.2, Problem 46E

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To factor: The expression 12 x 2 + 47 x y − 4 y 2 completely.

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To factor: The expression 12x2+47xy−4y2 completely.

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