# How do I use the factor theorem to prove x-2 must be a factor of 2x^3-x^2-7x+2?

Mar 17, 2018

$\text{see explanation}$

#### Explanation:

$\text{for a polynomial } f \left(x\right)$

• " if "f(a)=0" then "(x-a)" is a factor of "f(x)

$\text{substitute "x=2 " into the polynomial}$

$\Rightarrow 2 {\left(2\right)}^{3} - {\left(2\right)}^{2} - 7 \left(2\right) + 2 = 0$

$\Rightarrow \left(x - 2\right) \text{ is a factor of } 2 {x}^{3} - {x}^{2} - 7 x + 2$