# How do you use the remainder theorem to see if the x+6 is a factor of x^5+6x^4-3x^2-22x-29?

Feb 17, 2017

See explanation.

#### Explanation:

According to the Reminder theorem to see if $\left(x - a\right)$ is a factor of a polynomial $P \left(x\right)$ you have to check if $P \left(a\right) = 0$

In the given example we have:

$P \left(x\right) = {x}^{5} + 6 {x}^{4} - 3 {x}^{2} - 22 x - 29$ and $a = - 6$, so:

$P \left(- 6\right) = {\left(- 6\right)}^{5} + 6 \cdot {\left(- 6\right)}^{4} - 3 \cdot {\left(- 6\right)}^{2} - 22 \cdot \left(- 6\right) - 29$

$= - 7776 + 7776 - 108 + 132 - 29 = 132 - 108 - 29 =$

$= 24 - 29 = - 5$

The value $P \left(- 6\right)$ is different from zero, so the polynomial is not divisible by $\left(x + 6\right)$