# How do you use the remainder theorem to see if the n+2 is a factor of n^4+10n^3+21n^2+6n-8?

Jan 14, 2017

$n + 2$ is a factor of the given polynomial

#### Explanation:

The remainder theorem states that the bynomial $\left(x - a\right)$ is a factor of a polynomial P(x) if P(a)=0.

Let it be

$P \left(n\right) = {n}^{4} + 10 {n}^{3} + 21 {n}^{2} + 6 n - 8$,

then

$P \left(- 2\right) = {\left(- 2\right)}^{4} + 10 \cdot {\left(- 2\right)}^{3} + 21 \cdot {\left(- 2\right)}^{2} + 6 \cdot \left(- 2\right) - 8$

$= 16 - 80 + 84 - 12 - 8 = 0$

Then $n + 2$ is a factor of the given polynomial