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 t 2 − 15 t + 4 as follows. It is observed that, the coefficients are a = 9 , b = − 15 and c = 4 . Step 1: Find the value of a c . Obtain the value of a c as, a c = 9 ( 4 ) = 36 Thus, the value of a c is 36. Step 2: Find the two number, e and f, whose product is a c = 36 and whose sum is b = − 15 . Obtain the list of integer factors of 36 such that product is 36 and sum is –15 as shown below in Table 1. Integers whose product is 36 1 , 36 − 36 , − 1 − 6 , − 6 6 , 6 − 12 , − 3 Sum 37 –37 –12 12 –15 Table 1 From Table 1, it is observed that the numbers whose product is 36 and sum is –15 are − 12 and − 3 . Let, the variables e = − 12 and f = − 3

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ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 6.2, Problem 39E

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To factor: The given expression 9t2−15t+4 completely.

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Chapter 6.2, Problem 38E

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To factor: The given expression 9 t 2 − 15 t + 4 completely.

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