How would you divide (4w^2 + 4w - 1) / (2w+3 )

I'm new at this and I am asked to divide (4w^2 + 4w - 1) / (2w+3 ). I know your suppose to look for the Greatest Common Factor but I don't believe there is one for this question so what would the answer be?

You don't look for GCF. Use long polynomial division!

. . . . . . .2w - 1
. . . . . ._ _ _ _ _ _ _
2w + 3 | 4w² + 4w - 1
. . . . . .- 4w² - 6w
. . . . . . . . . . -2w - 1
. . . . . .. . . . . 2w + 3
. . . . . .. . . . . . . . .2

Therefore, the answer is (2w - 1) + 2/(2w + 3)

I hope this helps!

There are some cases where you can find a greatest common factor but not this one. You can use the comparing coefficients method instead, as shown.

(4w² + 4w - 1) / (2w + 3) = Aw + B + C / (2w + 3)
4w² + 4w - 1 = Aw(2w + 3) + B(2w + 3) + C
4w² + 4w - 1 = 2Aw² + 3Aw + 2Bw + 3B + C
4w² + 4w - 1 = 2Aw² + (3A + 2B)w + (3B + C)
2A = 4
A = 2
3A + 2B = 4
6 + 2B = 4
2B = -2
B = -1
3B + C = -1
-3 + C = -1
C = 2
(4w² + 4w - 1) / (2w + 3) = 2w - 1 + 2 / (2w + 3)

You would have to use long division or synthetic division