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 15 x 2 − 39 x 3 + 18 x 4 as follows. Rewrite the expression as, 15 x 2 − 39 x 3 + 18 x 4 = 3 x 2 ( 6 x 2 − 13 x + 5 ) (1) Consider the expression 6 x 2 − 13 x + 5 . It is observed that, the coefficients are a = 6 , b = − 13 and c = 5 . Step 1: Find the value of a c . Obtain the value of a c as, a c = 6 ( 5 ) = 30 Thus, the value of a c is 30. Step 2: Find the two number, e and f, whose product is a c = 30 and whose sum is b = − 13 . Obtain the list of integer factors of 30 such that product is 30 and sum is –13 as shown below in Table 1. Integers whose product is 30 1 , 30 − 1 , − 30 2 , 15 10 , 3 − 10 , − 3 − 2 , − 15 Sum 31 –31 17 13 –13 –17 Table 1 From Table 1, it is observed that the numbers whose product is 30 and sum is –13 are − 3 and − 10 . Let the variables e = − 3 and f = − 10 . Step 3: Write a x 2 + b x + c = a x 2 + m x + n x + c

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Author: Washington

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Chapter 6.2, Problem 52E

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To factor: The expression 15x2−39x3+18x4 completely.

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Chapter 6.2, Problem 51E

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Chapter 6 Solutions

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To factor: The expression 15 x 2 − 39 x 3 + 18 x 4 completely.

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To factor: The expression 15x2−39x3+18x4 completely.

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