# How do you factor 14x^2 + 29x - 15?

May 29, 2015

If $14 {x}^{2} + 29 x - 15$
$= \left(a x + b\right) \left(c x - d\right) \textcolor{w h i t e}{\text{XXXXX}}$we know there needs to be a 'minus' on the $d$ because of the 'minus' on $15$

then we are looking for

• factors $a \mathmr{and} c$ of $14$, and
• factors $b \mathmr{and} d$ of $15$
such that $b c - a d = 29$

Fortunately there are not a lot of factor pairs for $14 \mathmr{and} 15$
so we can quickly come up with
$\left(2 x + 5\right) \left(7 x - 3\right)$