# How do you factor the trinomial 7u^2+26u-8?

Oct 21, 2016

$\left(7 u - 2\right) \left(u + 4\right)$

#### Explanation:

$\textcolor{red}{7} {u}^{2} + \textcolor{b l u e}{26} u \textcolor{red}{- 8}$

For expansion, first
multiply $\textcolor{red}{7}$ with $\textcolor{red}{- 8}$, which is $= - 56$, then

Find 2 numbers whose product is $- 56$ and sum is $\textcolor{b l u e}{26}$, that is $\textcolor{g r e e n}{28}$ and $\textcolor{g r e e n}{- 2}$.

Factorization by expansion :
$7 {u}^{2} + \textcolor{g r e e n}{28 u - 2 u} - 8$

Now, take common on first 2 terms and last 2 terms seperately,
$7 u \left(u + 4\right) - 2 \left(u + 4\right)$

Further, taking common on $\left(u + 4\right)$:
$\left(7 u - 2\right) \left(u + 4\right)$