How do you factor 8u^2 + 6u - 9?

Jun 16, 2015

$8 {u}^{2} + 6 u - 9 = \left(2 u + 3\right) \left(4 u - 3\right)$

Explanation:

We need to look at factors of
$\textcolor{w h i t e}{\text{XXXX}}$$8$
$\textcolor{w h i t e}{\text{XXXX}}$$\left(a , b\right) \epsilon \left\{\begin{matrix}1 & 8 \\ 2 & 4\end{matrix}\right\}$
and
$\textcolor{w h i t e}{\text{XXXX}}$$\left(- 9\right)$
$\textcolor{w h i t e}{\text{XXXX}}$$\left(c , d\right) \epsilon \left\{\begin{matrix}1 & - 9 \\ - 1 & 9 \\ 3 & - 3 \\ - 3 & 3\end{matrix}\right\}$

such that
$\textcolor{w h i t e}{\text{XXXX}}$$a c - b d = + 6$

then plug them into
$\textcolor{w h i t e}{\text{XXXX}}$$\left(a u + c\right) \left(b u + d\right)$