# How do you factor 2m^2 - 11m + 15?

Mar 7, 2018

$\left(m - 3\right) \left(2 m - 5\right)$

#### Explanation:

Here's a way to do it...
$2 {m}^{2} - 11 m + 15$
Multiply the squared value with 15
${m}^{2} - 11 m + 30$
Factor normally...
$\left(m - 6\right) \left(m - 5\right)$
divide both values by 2
$\left(m - 3\right) \left(2 m - 5\right)$
5/2 won't be a whole number, so move that number before the $m$

Mar 7, 2018

(2m - 5)(m - 3)

#### Explanation:

Use the new AC Method (Socratic Search)
$f \left(m\right) = 2 {m}^{2} - 11 m + 15 =$ a(m + p)(m + q)
Converted trinomial:
$f ' \left(m\right) = {m}^{2} - 11 m + 30 =$ (m + p')(m + q')
Find p' and q', knowing the sum (-11) and the product (30).
They are: p' = - 5, and q' = - 6
Back to f(m) --> $p = \frac{p '}{a} = - \frac{5}{2}$, and $q = - \frac{6}{2} = - 3$.
Factored form:
$f \left(m\right) = 2 \left(m - \frac{5}{2}\right) \left(m - 3\right) = \left(2 m - 5\right) \left(m - 3\right)$