# How do you factor the trinomial 15m^2 + 19m + 6?

Dec 23, 2015

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

#### Explanation:

first make sure the coefficient of ${m}^{2}$ is 1
you can factorize a quadratic polynomial in the form:
${m}^{2} +$(sum of two numbers)$m +$(product of two numbers)
let the two numbers be $a , b$
so, from the equation, we have
$a + b = \frac{19}{15}$ & $a \cdot b = \frac{6}{15}$

solve this 2 equation 2 unknown by substituting either $a = \frac{6}{15 b}$ or $b = \frac{6}{15 a}$ into the eq $a + b = \frac{19}{15}$
on solving you get the two numbers $a$ & $b$ as $\frac{2}{3} , \frac{3}{5}$
now, you can write:
${m}^{2} + \left(\frac{2}{3} + \frac{3}{5}\right) m + \left(\frac{2}{3} \cdot \frac{3}{5}\right)$
${m}^{2} + \frac{2}{3} m + \frac{3}{5} m + \left(\frac{2}{3} \cdot \frac{3}{5}\right)$
$m \left(m + \frac{2}{3}\right) + \frac{3}{5} \left(m + \frac{2}{3}\right)$
$\left(m + \frac{2}{3}\right) \cdot \left(m + \frac{3}{5}\right)$