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

Feb 2, 2017

$\left(x - 1\right)$ is not a factor

#### Explanation:

We use the remainder theorem

When we divide a polynomial $f \left(x\right)$ by $\left(x - c\right)$,

$f \left(x\right) = \left(x - c\right) q \left(x\right) + r \left(x\right)$

When $x = c$

$f \left(c\right) = r$

If $\left(x - c\right)$ is a factor $f \left(c\right) = 0$

So, here

$f \left(x\right) = 2 {x}^{3} - {x}^{2} - 3 x - 2$

$f \left(1\right) = 2 - 1 - 3 - 2 = - 4$

Therefore,

the remainder is $= - 4$

So, $\left(x - 1\right)$ is not a factor of $f \left(x\right)$