# 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...
 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: $$(t)(1/2t^2-5t+3)+36 = 0$$ But the jump to t-4 has got me stumped! Any pointers to threads/websites on factoring polynomials/finding roots of polynomials would be most appreciated.