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 b T 2 − 40 b T + 400 b as follows. Rewrite the expression as, b T 2 − 40 b T + 400 b = b ( T 2 − 40 T + 400 ) (1) Consider the expression T 2 − 40 T + 400 . It is observed that, the coefficients are a = 1 , b = − 40 and c = 400 . Step 1: Find the value of a c . Obtain the value of a c as, a c = 1 ( 400 ) = 400 Thus, the value of a c is 400. Step 2: Find the two number, m and n, whose product is a c = 400 and whose sum is b = − 40 . Obtain the list of integer factors of 400 such that product is 400 and sum is –40 as shown below in Table 1. Integers whose product is 400 1 , 400 20 , 20 − 20 , − 20 − 1 , − 400 Sum 401 40 –40 –401 Table 1 From Table 1, it is observed that the numbers whose product is 400 and sum is –40 are − 20 and − 20 . Let, the integers take the variables m = − 20 and n = − 20 . Step 3: Write a x 2 + b x + c = a x 2 + m x + n x + c

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 6.2, Problem 60E

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To factor: The expression bT2−40bT+400b completely.

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Chapter 6.2, Problem 59E

Chapter 6.2, Problem 61E

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Chapter 6 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

Ch. 6.1 - Prob. 1PE Ch. 6.1 - Prob. 2PE Ch. 6.1 - Prob. 3PE Ch. 6.1 - Prob. 4PE Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E

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To factor: The expression b T 2 − 40 b T + 400 b completely.

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To factor: The expression bT2−40bT+400b completely.

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Chapter 6 Solutions