Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 6 - Section 6.2 - Factoring Trinomials of the Form x2+bx+c - Exercise Set: 83

Answer

Chapter 6 - Section 6.2 - Exercise Set: 83 (Answer) $-16t^2 + 64t + 80$ = $-16(t + 1)(t - 5)$

Work Step by Step

Chapter 6 - Section 6.2 - Exercise Set: 83 (Solution) Factorize : $-16t^2 + 64t + 80$ First step : Take out the GCF of $-16t^2$, $64t$ and $80$ which is $-16$ $-16t^2 + 64t + 80$ = $-16(t^2 - 4t - 5)$ Take $(t^2 - 4t - 5)$ to be $(t + \triangle)(t + \square)$ For this, we have to look for two numbers whose product is -5 and whose sum is -4. Factors of -5 $\Longleftrightarrow$ Sum of Factors 1,-5 $\Longleftrightarrow$ -4 (Correct sum, the two numbers are 1 and -5) 5,-1 $\Longleftrightarrow$ 4 (Incorrect sum) Thus, $(t^2 - 4t - 5)$ = $(t + 1)(t - 5)$ And, $-16t^2 + 64t + 80$ = $-16(t + 1)(t - 5)$
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