In order to factor the given expression we have to start by determining the greatest common factor (GCF) of the terms of the given function, like this:
-16t² = -1×16×t×t
128t = 8×16×t
Then, 16t is the greatest common factor, by factoring 16t out we get:
h(t) = 16t(-1×t + 8)
By factoring -1 out, we get:
h(t) = -16t(t - 8)
Then, the factored expression is h(t) = -16t(t - 8)
By evaluating the factored expression at t = 2, we get:
h(2) = -16(2)(2 - 8) = -16(2)(-6) = 192
For the base expression:
h(2) = -16(2)² + 128(2) = 192
We got 192 from both expressions at t = 2, then the factored expression was correctly formulated