# How do you factor completely: 2x^2 + 13x + 15?

Jul 22, 2015

$2 \left(x + \frac{3}{2}\right) \left(x + 5\right)$

#### Explanation:

$a {x}^{2} + b x + c = a \left(x - {x}_{1}\right) \left(x - {x}_{2}\right)$

$2 {x}^{2} + 13 x + 15 = 0$

x_i = (- 13 ± sqrt{13^2 - 4 * 2 * 15}) / 4

${x}_{1} = \frac{- 13 + 7}{4} = - \frac{3}{2}$

${x}_{2} = \frac{- 13 - 7}{4} = - 5$

Jul 23, 2015

Factor y = 2x^2 + 13x + 15

#### Explanation:

I use the new AC Method to factor trinomials (Google, Yahoo Search).
$y = 2 {x}^{2} + 13 x + 15 =$ 2(x - p)(x - q)
Converted $y ' = {x}^{2} + 13 x + 30 =$(x - p')(x - q').
Factor pairs of ac = 30 -> (2, 15)(3, 10). this sum is 13 = b.
Then, p' = 3 and q' = 10.
Then, $p = \frac{3}{2}$ and $q = \frac{10}{2} = 5.$
Factored form: $y = 2 \left(x + \frac{3}{2}\right) \left(x + 5\right) = \left(2 x + 3\right) \left(x + 5\right)$