Factoring 9y^2+9y-4 where to begin?

[Guest]

i am trying to factor this and i really don't understand how... the questions before it had common factors.. but .. this one doesen't i think the awnser is (-3y-4)(-3y+1) but i am not shure.. any help is greatly apreciated

 

[tkhunny]

You can always multiply and check. In this case, you'll get the 9y^2 and the -4, but the middle term needs help.

Completing the square can be helpful.

9y^2 + 9y - 4 = 9(y^2 + y + ________) - 4 - 9*_____________

1/2 = 1/2
(1/2)^2 = 1/4

9(y^2 + y + 1/4) - 4 - 9*(1/4)
9*(y+1/2)^2 - 25/4

That is a difference of squares. You should recognize that and how to factor it.

 

[soroban]

Hello, bobby2110!

I am trying to factor 9y² + 9y - 4 and i really don't understand how.

The questions before it had common factors, but this one doesen't.
I think the answer is (-3y - 4)(-3y + 1) but i am not sure.

Going from "common factors" to this problem is a HUGE leap.
. . Are you <u>sure</u> there aren't any problems in-between?

Usually, they would introduce "Factoring Trinomials" with an easier problem first ...
. . like: y² - 6y + 8, with a leading coefficient of 1.

Your factoring is correct, but they usually don't use "two negatives".
. . The expected answer is: .(3y + 4)(3y - 1)

Although (-3y)(-3y) = 9y², why would you want to introduce negatives?

Given: .4x + 6y . . . Would you factor out -2 . . . and get: .-2(-2x - 3y) ?
. . Technically, it's correct . . . but somewhat clumsy, isn't it?