# How do you factor 7(x^2) - 19x - 6?

Sep 30, 2015

$\left(7 x + 2\right) \left(x - 3\right)$

#### Explanation:

$7 {x}^{2} - 19 x - 6 = \left(7 x + 2\right) \left(x - 3\right)$

Sep 30, 2015

Factor $y = 7 {x}^{2} - 19 x - 6$

Ans: (7x + 2)(x - 3)

#### Explanation:

y = a(x + p)(x + q)
I use the new AC Method to factor trinomials (Socratic Search).
Converted trinomial: $y ' = {x}^{2} - 19 x - 42 =$ (x + p')(x + q'). p' and q' have opposite signs, Factor pairs of (-42) -->(-2, 21). This sum is 19 = -b. The opposite sum gives: p' = 2 and q' = -21.
Therefor: $p = \frac{2}{7}$ and $q = - \frac{21}{7} = - 3$.
The factored form is: $y = 7 \left(x + \frac{2}{7}\right) \left(x - 3\right) = \left(7 x + 2\right) \left(x - 3\right)$