# How do you factor completely 3y^2 - 4y - 15 ?

Dec 13, 2015

Factor $f \left(y\right) = 3 {y}^{2} - 4 y - 15$

Ans: (3y + 5)(y - 3)

#### Explanation:

Use the new AC method to factor trinomials (Socratic Search)
$f \left(y\right) = 3 {y}^{2} - 4 y - 15 =$ 3(y + p )(y + q)
Converted trinomial $f ' \left(y\right) = {y}^{2} - 4 y - 45 =$(y + p')( + q').
p' and q' have opposite signs. Factor pairs of (-45) --> (-3, 15)(-5, 9). This sum is 9 - 5 = 4 = -b. Then, the opposite sum gives: p' = 5 and q' = - 9.
Back to f(y), $p = \frac{p '}{a} = \frac{5}{3}$ and $q = \frac{q '}{a} = - \frac{9}{3} = - 3$.
Factored form: f(y) = 3(y + 5/3)(y - 3) = (3y + 5)(y - 3).