# How do you factor 24y^2 + 41y + 12?

Aug 6, 2015

Factor f(y) = 24y^2 + 41y + 12

Ans: (8x + 3)(3x + 4)

#### Explanation:

$y = 24 {y}^{2} + 41 y + 12 =$24(x - p)(x - q)
I use the new AC Method (Google, Yahoo Search)
Converted trinomial $y ' = {x}^{2} + 41 x + 288 =$ (x - p')(x - q')
p' and q' have same sign (Rule of signs)
Factor pairs of 288 --> ...(6, 48)(8, 36)(9, 32). This sum is 41 = -b.
Then p' = 9 and q' = 32
Therefor, $p = \frac{p '}{a} = \frac{9}{24} = \frac{3}{8}$, and $q = \frac{q '}{a} = \frac{32}{24} = \frac{4}{3.}$

Factored form: $y = 24 \left(x + \frac{3}{8}\right) \left(x + \frac{4}{3}\right) = \left(8 x + 3\right) \left(3 x + 4\right)$

NOTE. Solving by the new AC Method is fast, systematic, no guessing, no lengthy solving by grouping.