# How do you use the remainder theorem to find the remainder for each division (2x^3-3x^2+x)div(x-1)?

May 17, 2017

$0$

#### Explanation:

The remainder theorem states that if you divide $P \left(x\right)$ by $\left(x - a\right)$

the remainder will be $P \left(a\right)$

so dividing $P \left(x\right) = \left(2 {x}^{3} - 3 {x}^{2} + x\right) \text{ }$by $\text{ } \left(x - 1\right)$

will give a remainder of $P \left(1\right)$

$P \left(1\right) = 2 \times {1}^{3} - 3 \times {1}^{2} + 1$

$P \left(1\right) = 2 - 3 + 1 = 0$

which means that in this case $\left(- 1\right)$ is a factor of $P \left(x\right)$