# What is the GCF of the terms of the polynomial 8x^6+32x^3?

Dec 7, 2017

$8 {x}^{3}$

#### Explanation:

You can divide $8 {x}^{3}$ from both $8 {x}^{6}$ and $32 {x}^{3}$.

$8 {x}^{6} + 32 {x}^{3} = 8 {x}^{3} \left({x}^{2} + 4\right)$

You cannot factor more.

Dec 7, 2017

$8 {x}^{3}$

#### Explanation:

If a GCF is not immediately obvious, I like to just start, and as I go I usually find more:

$8 {x}^{6} + 32 {x}^{3}$

Let's take out an $8$

$8 \left({x}^{6} + 4 {x}^{3}\right)$

Now let's see what we can do about those variables; let's remove ${x}^{3}$

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

There are no other common factors, so $8 {x}^{3}$ is the GCF of $8 {x}^{6} + 32 {x}^{3}$