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, $-16t^2 + 64t + 80$ = $-16(t + 1)(t - 5)$
