# How do you factor 3v^2+14v+8 ?

May 16, 2015

$y = 3 {v}^{2} + 14 v + 8.$= (x - p)(x - q)
I use the new AC Method to factor trinomials (Google, Yahoo Search)

Converted trinomial: $y ' = {v}^{2} + 14 v + 24 =$ (x -p')(x - q') (a,c = 24)
Compose factor pairs of 24: (1, 24)(2, 12). This sum is 14 = b. Then
p' = 2 and q' = 12. Back to original trinomial: $p = \frac{p '}{a} = \frac{2}{3}$, and $q = \frac{q '}{a} = \frac{12}{3} = 4.$

Factored form: $y = \left(x + \frac{2}{3}\right) \left(x + 4\right) = \left(3 x + 2\right) \left(x + 4\right)$

Check by developing
y = 3x^2 + 12x + 2x + 8) = 3x^2 + 14x + 8 . OK