# Factoring problem that has me stumped!

by crookesm
Tags: factoring, stumped
 P: 5 Given: $$s(t) = 1/2t^3-5t^2+3t+6$$ I'm trying to find all values of t where s(t) = -30 My first thought is to solve for 0 hence: $$1/2t^3-5t^2+3t+36=0$$ I know the answers are t=4 and t=8.196 but I can't get to it...I'm assuming I need to factor this down but I'm can't see it. Any help/hints would be most appreciated as I've been banging my head against a brick wall for some time now...
 PF Patron HW Helper Sci Advisor Thanks P: 11,935 You know that 4 is a root of the polynomial in your last equation. Use polynomial division to compete the factoring.
 P: 18 As above, but divide (x-4) into 1/2t^3-5t^2+3t+36 Then when you get the second polynomial use the quadratic solution to get t=8.196
P: 5

## Factoring problem that has me stumped!

Thanks for the hints - reading up on polynomial division (which I wasn't familiar with) I have found that the factors are:

$$(t-4)(1/2t^2-3t-9)$$

However, (and I realise I'm getting slightly off topic here) how would I even arrive at (t-4) being one of the original factors. Using GCF I can easily see that:

$$(t)(1/2t^2-5t+3)+36 = 0$$