# How do you determine whether x-1 is a factor of the polynomial 2x^3+4x^2-5x-1?

Feb 15, 2017

$\left(x - 1\right)$ is a factor of $p \left(x\right)$.

#### Explanation:

Let us denote the poly. by $p \left(x\right) , s o , p \left(x\right) = 2 {x}^{3} + 4 {x}^{2} - 5 x - 1.$

A very simple test to check whether $\left(x - 1\right)$ is a factor of $p \left(x\right) :$ is

$\left(x - 1\right) \text{ is a factor of "p(x) iff" the sum of the co-effs. of "p(x)" is zero.}$

Here, in our Example, the sum of co-effs. of

$p \left(x\right) = 2 + 4 - 5 - 1 = 0$

Hence, $\left(x - 1\right)$ is a factor of $p \left(x\right)$.