# How do you use the factor theorem to determine whether b+1 is a factor of b^6 – b^5 – b + 1?

Dec 13, 2015

$b + 1$ is NOT the factor of ${b}^{6} - {b}^{5} - b + 1$

#### Explanation:

To check if $\left(x - a\right)$ is a factor of $P \left(x\right)$ you have to check if $P \left(a\right) = 0$

In this case $a = - 1$ so you have to find $P \left(- 1\right)$

$P \left(- 1\right) = {\left(- 1\right)}^{6} - {\left(- 1\right)}^{5} - \left(- 1\right) + 1 = 1 + 1 + 1 + 1 = 4$

$P \left(- 1\right) \ne 0$, so $\left(x + 1\right)$ is NOT the factor of $P \left(x\right)$