# How do you factor  2a^3+4a^2+8a?

Jun 14, 2018

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

#### Explanation:

We immediately recognize that al terms have an $a$ in common, so we can factor that out. We get

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

We also notice that all of the terms I have in blue have a $2$ in common that we can factor out. Doing this, we now have

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

What I have in blue, let's think for a moment:

Are there any two numbers that sum up to $2$ and have a product of $4$?

You may have got stuck. There are no such numbers. This means this is the most we can factor this expression with real numbers. Our answer is

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

Hope this helps!

Jun 14, 2018

See a solution process below:

#### Explanation:

Factor a $\textcolor{red}{2 a}$ form each term in the expression:

$2 {a}^{3} + 4 {a}^{2} + 8 a \implies$

$\left(\textcolor{red}{2 a} \cdot {a}^{2}\right) + \left(\textcolor{red}{2 a} \cdot 2 a\right) + \left(\textcolor{red}{2 a} \cdot 4\right) \implies$

$\textcolor{red}{2 a} \left({a}^{2} + 2 a + 4\right)$

The term within the parenthesis cannot be factored further.