How do you factor 8x³+4x²-2x-1?

Dec 13, 2015

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

Explanation:

"Group" the polynomial into two parts:

$\textcolor{b l u e}{8 {x}^{3} + 4 {x}^{2}} \textcolor{red}{- 2 x - 1}$

Factor out a common term from either section.

$\textcolor{b l u e}{4 {x}^{2} \left(2 x + 1\right)} \textcolor{red}{- 1 \left(2 x + 1\right)}$

Notice that a $2 x + 1$ term can be factored out.

(2x+1)color(purple)((4x^2-1)

Notice that $4 {x}^{2} - 1$ is a difference of squares.

$\left(2 x + 1\right) \textcolor{p u r p \le}{\left(2 x + 1\right) \left(2 x - 1\right)}$

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