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

Feb 27, 2017

$\left(x + 2\right) \text{ is not a factor of the poly.}$

#### Explanation:

As per the Factor Theorem,

$\left(p x + q\right) \text{ is a Factor of a Poly. } f \left(x\right) \iff f \left(- \frac{q}{p}\right) = 0.$

We have, $\left(p x + q\right) = x + 2 , \text{ so that, "p=1, q=2," whence, } - \frac{q}{p} = - 2 , \mathmr{and} , f \left(x\right) = {x}^{4} - 2 {x}^{2} + 3 x - 4.$

$\therefore f \left(- \frac{q}{p}\right) = f \left(- 2\right) = {\left(- 2\right)}^{4} - 2 {\left(- 2\right)}^{2} + 3 \left(- 2\right) - 4$

$= 16 - 8 - 6 - 4 = - 2 \ne 0.$

$\therefore \left(x + 2\right) \text{ is not a factor of the poly. } f \left(x\right) .$