Question

Can someone please factor the following expression...3y^3-9y^2+4y-12? Thank you!

Answer 1

No, unfortunately I do not?

Answer 2

Nevermind, ignore that. This can be done by factoring by grouping.

Answer 3

So you want to split your four terms into 2 groups of two. From each of those 2 groups, you would factor out the greatest common factor.

Answer 4

so 3y^3-9y^2 and 4y-12. The greatest common factor of 3 and 9 is 3 and of 4 and 12 is 4, right? So then what?

Answer 5

Alright, so that would give you:
3(y^3-3y^2) 4(y-3)
Now, you should have the remaining things in parenthesis match after you do this, but we dont. That first group of terms, though, you can also factor out a power of y.

Answer 6

Gtg for now, unfortunately. But you would always need to factor a variable to a power from one group when you do this. So the first group can also factor out a y^2, giving:
3y^2(y-3) + 4(y-3). Now you should always have those parenthesis groups match, which we do, both (y-3). Once you do this, you have two factor. One factor is the parenthesis group that appears twice, the (y-3). The second factor is a combination of the greatest common factors that were factored out, so 3y^2 and 4. So this gives a final factoring then of:
(3y^2+4)(y-3)

Answer 7

Ok, that makes perfect sense. I got the same thing finally. Thank you so much for all of the help!