# How do you factor # (15x²+22x-5)?

May 4, 2015

In an attempt to find integer based factors:
We are looking for factors of 15 $\left(a \times b\right)$
and factors of 5 $\left(c \times d\right)$
such that $a c - b d = 22$

There are only a very few factors available and we should soon come up with $\left(a , b\right) = \left(5 , 3\right)$ and $\left(c , d\right) = \left(5 , 1\right)$

Since the final term of the given expression is negative, one of $\left(5 , 1\right)$ needs to be negative;
furthermore, since the coefficient of the middle term is positive
5 must be the positive value and 1 the negative.

Factors:
$15 {x}^{2} + 22 x - 5 = \left(5 x - 1\right) \left(3 x + 5\right)$