# How do you factor 12x^4 + 11x^3 -26x^2 + x + 2?

Oct 2, 2016

$\left(x + 2\right) \left(12 {x}^{3} - 13 {x}^{2} + 1\right)$

#### Explanation:

There are 5 terms, so we will have to group them first.
The first 3 terms have an obvious factor of ${x}^{2}$
Let's try with those...

$\textcolor{red}{\left(12 {x}^{4} + 11 {x}^{3} - 26 {x}^{2}\right)} + \left(x + 2\right)$

$= \textcolor{red}{{x}^{2}} \left(12 {x}^{2} + 11 x - 26\right) + \left(x + 2\right)$

$= {x}^{2} \left(12 x - 13\right) \textcolor{b l u e}{\left(x + 2\right)} + \textcolor{b l u e}{\left(x + 2\right)}$

$= \textcolor{b l u e}{\left(x + 2\right)} \left({x}^{2} \left(12 x - 13\right) + 1\right)$

$= \left(x + 2\right) \left(12 {x}^{3} - 13 {x}^{2} + 1\right)$