How do i factor 9t^2+5t-4 using the "ac" method?

Answer 1

I love the AC method because it gives rules to follow.
1) Take out the common factor. There is none here.

2) multiply a times c which is 9 times -4 = -36

3) Find factors of -36 that will add up to 5

2 times -18 adds to -16 NO

4 times - 9 adds to -5 NO

-4 times 9 adds to 5

replace 5t with -4t+ 9t

The order doesn't matter, but it is easier in the next step if you put the negative term first.

9t^2 -4t + 9t -4

I went back to the original equation and put in -4t and 9t for the 5t

Factor by grouping!
(9t^2 -4t) + (9t -4)

t(9t -4) + 1(9t-4)

I just took out what was common. It is important to write down the "1" if nothing else is common.

Now, you actually factor out the (9t-4). I tell my students that the factor that is there twice gets written down once. What is left over is the other factor. (9t-4)(t+1)

If you took out a common factor in the first step, this is where you would put it in front of the first factor.
You should always multiply these two factors as a check to be sure you did factor correctly. When you multiply you should get your original trinomial

Answer 2

y^3+y^2-4y-4