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 9 x 2 + 7 x y − 2 y 2 as follows. Consider the expression 9 x 2 + ( 7 y ) x − 2 y 2 , where x is variable and y is constant. It is observed that, the coefficients are a = 9 , b = 7 y and c = − 2 y 2 . Step 1: Find the value of a c . Obtain the value of a c as, a c = 9 ( − 2 y 2 ) = − 18 y 2 Thus, the value of a c is − 18 y 2 . Step 2: Find the two number, m and n, whose product is a c = − 18 y 2 and whose sum is b = 7 y . Obtain the list of integer factors of − 18 y 2 such that product is − 18 y 2 and sum is 7 y as shown below in Table 1. Integers whose product is − 18 y 2 y , − 18 y 2 y , − 9 y − 2 y , 9 y − 6 y , 3 y 6 y , − 3 y Sum –17 y –7 y 7 y –3 y 3 y Table 1 From Table 1, it is observed that the numbers whose product is − 18 y 2 and sum is 7 y are − 2 y and 9 y

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Author: Washington

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Chapter 6.2, Problem 33E

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To factor: The given expression 9x2+7xy−2y2 completely.

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Chapter 6.2, Problem 32E

Chapter 6.2, Problem 34E

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To factor: The given expression 9 x 2 + 7 x y − 2 y 2 completely.

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