# How do you factor by grouping #30x^2 + 76x + 48 #?

##### 2 Answers

How did I find a splitting of the middle

The coefficients of

We need to find a factorization of

If you like to avoid guessing, or avoid the lengthy factoring by grouping, use the systematic New AC Method.

Convert f(x) to f'(x) = x^2 + 38x + 360. = (x - p')(x - q'). Compose factor pairs of a.c = 360. a and c have same sign. Proceed:...(15, 24)(18, 20). OK. This sum is 18 + 20 = 38 = b. Then, p' = 18 and q' = 20

Then

Factored form: