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

Mar 23, 2017

See the entire solution process below:

Explanation:

First, rewrite the expression by grouping as:

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

Now factor each of these as:

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

#(x^2(x + 2)) + (4(x + 2))

We can now factor out the $\left(x + 2\right)$ term leaving:

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