Question

Can someone explain factoring this polynomial?

Answer 1

y^3+3y^2-2y-6

Answer 2

We have to use grouping right?

Answer 3

@Whitemonsterbunny17 @Elsa213 @mathstudent55

Answer 4

yes. It's never obvious (to me) what to look for.

but one hope is that we can group two pairs.

try
(y^3+3y^2) + (-2y-6)

Answer 5

now factor both pairs.

Answer 6

Okay so for the first we can factor out y^2 and on the second factor out 2

Answer 7

what do we get ?

Answer 8

(y) and (-y-3)

Answer 9

I hope you mean
(y^3+3y^2) + (-2y-6)
y^2 (y+3) + 2(-y-3)

Answer 10

yeah thats just how I thought about it in my head

Answer 11

we can make it -2(y+3) right?

Answer 12

notice the (y+3) and the (-y-3) look promising

Yes! -2(y+3)
so that we have
y^2 (y+3) - 2(y+3)

Answer 13

and of course (y+3) is in both terms, so it can be factored out

Answer 14

if we had
A y^2 - 2 A
we would factor out the A to get
A(y^2-2)

you can think of (y+3) as a "complicated" A

Answer 15

Oh okay, and sorry for the late reply it was lagging and wouldn't let me in

Answer 16

I understand this but sometimes its hard to see through the problem, any tips?

Answer 17

1) Look at the problem and try to remember if you have seen a similar one that you have done.
2) Practice
3) Practice
4) Practice

Answer 18

Okay, thanks a ton! :D

Answer 19

@phi one last question, whats the difference between what we just did, and factoring TRInomials?

Answer 20

trinomials are (in some ways) easier, because there is a fixed procedure to follow. However, the procedure is painful until you get good at it (it helps a lot to know by heart the addition and multiplication tables, which since calculators, people don't seem to do)

Answer 21

If you have time, you can watch some of Khan's videos.
http://www.khanacademy.org/math/algebra/multiplying-factoring-expression/factoring-quadratic-expressions/v/factoring-quadratic-expressions

Answer 22

I love khan hahaha :) soooottthhiinnngggg voice