Expert: Paul Klarreich - 2/15/2010

Question
I have one problem I can't figure out.  It is a "solving equations by factoring" question.

The problem is: -t^3-3t^2+4t+12.  The answer is -3,-2,2.  But I can't figure out how to get there.  

I mostly just need the set-up as this is the only problem on my homework with 4 terms and I don't see any GCFs or grouping ways to factor it.

Answer
Questioner: JanaLee
Country: United States
Category: Advanced Math
Private: No
Subject: Intermediate Algebra
Question: I have one problem I can't figure out.  It is a "solving equations by factoring" question.

The problem is: -t^3-3t^2+4t+12.  The answer is -3,-2,2.  But I can't figure out how to get there.  

I mostly just need the set-up as this is the only problem on my homework with 4 terms and I don't see any GCFs or grouping ways to factor it.
..........................................

-t^3 - 3t^2 + 4t + 12 = 0, you mean?

I can't answer without knowing what you are studying.  I mean EXACTLY what?

Have you learned:

Synthetic division.
The factor theorem.
The rational root theorem.

That is what is used here.

Write:

t^3 + 3t^2 - 4t - 12 << signs flipped.


Choices: +- 1,2,3,4,6.

Try x = 2:


1   3 -  4 - 12   (2)
   2   10   12
-----------------
1   5    6    0  << good.   x = 2 is a root.

Now solve   x^2 + 5x + 6 = 0