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 z 2 − 19 z + 6 as follows. It is observed that, the coefficients are a = 3 , b = − 19 and c = 6 . Step 1: Find the value of a c . Obtain the value of a c as, a c = 3 ( 6 ) = 18 Thus, the value of a c is 18. Step 2: Find the two number, m and n, whose product is a c = 18 and whose sum is b = − 19 . Obtain the list of integer factors of 18 such that product is 18 and sum is –19 as shown below in Table 1. Integers whose product is 18 1 , 18 2 , 9 3 , 6 − 1 , − 18 − 2 , − 9 − 3 , − 6 Sum 19 11 9 –19 –11 –9 Table 1 From Table 1, it is observed that the numbers whose product is 18 and sum is − 19 are − 1 and − 18

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ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 6.2, Problem 25E

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To factor: The given expression 3z2−19z+6 completely.

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To factor: The given expression 3 z 2 − 19 z + 6 completely.

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