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 3 Q 2 + Q − 30 as follows. It is observed that, the coefficients are a = 3 , b = 1 and c = − 30 . Step 1: Find the value of a c . Obtain the value of a c as, a c = 3 ( − 30 ) = − 90 Thus, the value of a c is –90. Step 2: Find the two number, m and n, whose product is a c = − 90 and whose sum is b = 1 . Obtain the list of integer factors of –90 such that product is –90 and sum is 1 as shown below in Table 1. Integers whose product is –90 1 , − 90 − 10 , 9 10 , − 9 − 1 , 90 Sum –89 –1 1 89 Table 1 From Table 1, it is observed that the numbers whose product is –90 and sum is 1 are − 9 and 10 . Let, the integers take the variables m = − 9 and n = 10

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Author: Washington

Publisher: PEARSON

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Chapter 6.2, Problem 59E

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Chapter 6.2, Problem 58E

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To factor: The expression 3 Q 2 + Q − 30 completely.

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To factor: The expression 3Q2+Q−30 completely.

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