# How do you factor 15x^2-19x+6?

Aug 5, 2015

Factor $y = 15 {x}^{2} - 19 x + 6$

Ans: (5x - 3)(3x - 2)

#### Explanation:

$y = 15 {x}^{2} - 19 x + 6 =$ 15(x - p)(x - q).
I use the new AC Method (Yahoo, Google Search)
Converted trinomial $y ' = {x}^{2} - 19 x + 90 =$ (x - p')(x - q')
Factor pairs of 90 -> ...(6, 15)(9, 10). This sum is 19 = -b. Then p' = -9 and q' = -10.
Then, $p = \frac{p '}{a} = - \frac{9}{15} = - \frac{3}{5}$ and $q = - \frac{10}{15} = - \frac{2}{3.}$

Factored form: $y = 15 \left(x - \frac{3}{5}\right) \left(x - \frac{2}{3}\right) = \left(5 x - 3\right) \left(3 x - 2\right)$