Question

Factor Completly:
3y^2+7y-20
I got (5y+12)(y-1)

Answer 1

You can check your answer by foiling.

(5y + 12)(y - 1)
5y^2 - 5y + 12y - 12
5y^2 + 7y - 12

That's not our original, so it hasn't been correctly factored.

3y^2 + 7y - 20
We know the first part of each bracket because there's only one option...

(3y )(y )
Now we have to imagine foiling as we figure this out. The last two numbers multiplied together must equal -20, but 3y*(first number) + y*(second number) has to be 7y.

For -20, we can have: 5 & 4, 10 & 2, or 20 & 1 (with one of the two numbers being negative).

As a general rule, usually choose the two numbers that are closest together. In this case, that is 5 & 4.

(3y 5)(y 4)
We just have to pick our signs now. We know one must be negative, and one must be positive (because multiplied together, they must equal -20).

(3y - 5)(y + 4)

And the check by foiling...
3y^2 + 12y - 5y - 20
3y^2 + 7y - 20

That's our original, so we got it right. It cannot be factored any further.