Question

what are the factors of x^3-2x^2-29x+30
Please explain the steps too?

Answer 1

I know the answers are (x-6) (x-1) (x+5) but how do I explain that?

Answer 2

Well you can foil those out or you can notice that \(1\) is a solution, and then divide the whole thing by \((x-1)\) then factor that.

Answer 3

Do you know how to do that?

Answer 4

yes thank you

Answer 5

1. use the rational root theorem
- find all factors of the last term in the polynomial
so in that case it's 30
. We need the positive and negative versions
1, 2, 3, 5, 6, 10, 15, 30
-1, -2, -3, -5, -6, -10, -15, -30
2. Plug in one of these numbers and see if our result is 0. If our result is 0, then we have found one of the roots. If not, then we continue until we find a number that can give us 0

For example, if we let x = 1
\[1^3-2(1^2)-29(1)+30 \rightarrow 1-2-29+30 =-30+30 = 0 \]

3.since we obtained one of the roots. Use long division or synthetic division to find the remaining roots.

Answer 6

I'm gonna use synthetic division because long division will take some time