# How do you factor 3x^2 + 7x + 2?

Mar 25, 2016

$y = 3 {x}^{2} + 7 x + 2 =$ 3(x = p)(x + q)
Converted trinomial $y ' = {x}^{2} + 7 x + 6 =$(x + p')(x + q')
Factor pair of (6) --> (1, 6). This sum is 7 = b. Then p' = 1 and q' = 6. Back to y, $p = \frac{1}{3}$ and $q = \frac{6}{3} = 2.$
$y = 3 \left(x + \frac{1}{3}\right) \left(x + 2\right) = \left(3 x + 1\right) \left(x + 2\right)$