How do you factor by grouping x^3+4x^2+8x+32?

May 29, 2018

$\left({x}^{2} + 8\right) \left(x + 4\right)$

Explanation:

Factor each half of the expression individually first:

$\implies {x}^{2} \textcolor{b l u e}{\left(x + 4\right)} + 8 \textcolor{b l u e}{\left(x + 4\right)}$

Hence $\left(x + 4\right)$ is common in each term, factor this out:

$\implies \textcolor{b l u e}{\left(x + 4\right)} \left[{x}^{2} + 8\right]$

color(red)(= (x^2 + 8 ) ( x + 4)

In terms of real numbers, this is factorised

May 29, 2018

$\left(x + 4\right) \left({x}^{2} + 8\right)$

Explanation:

$= \textcolor{red}{{x}^{2}} \left(x + 4\right) \textcolor{red}{+ 8} \left(x + 4\right)$

$\text{take out the "color(blue)"common factor } \left(x + 4\right)$

$= \left(x + 4\right) \left(\textcolor{red}{{x}^{2} + 8}\right)$

${x}^{3} + 4 {x}^{2} + 8 x + 32 = \left(x + 4\right) \left({x}^{2} + 8\right)$