Final answer:
To write the polynomial (-16t^2 + 16t + 32) feet in factored form, we can start by factoring out the common factor 16. Then, we need to factor the quadratic expression inside the parentheses. The factored form of the polynomial is 16(-t - 2)(t - 1).
Step-by-step explanation:
To write the polynomial (-16t^2 + 16t + 32) feet in factored form, we need to factor out the common factor from each term. The common factor here is 16, so we can rewrite the polynomial as 16(-t^2 + t + 2). Now, let's factor the quadratic expression inside the parentheses.
To factor the quadratic expression -t^2 + t + 2, we need to find two binomials whose product is -t^2 + t + 2. We can set up the factored form as (at + b)(ct + d) and expand it using FOIL: (at)(ct) + (at)(d) + (b)(ct) + (b)(d).
The factors of -t^2 + t + 2 can be found by finding two numbers whose product is ac (which is -1), and whose sum is b (which is 1). The numbers that fit these conditions are -1 and -2, so the factored form of the polynomial is 16(-t - 2)(t - 1).