Question

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

Answer 1

`(x+2)" is not a factor of the poly."`

Explanation:

As per the Factor Theorem,

`(px+q)" is a Factor of a Poly. "f(x) iff f(-q/p)=0.`

We have, `(px+q)=x+2," so that, "p=1, q=2," whence, "-q/p=-2, and, f(x)=x^4-2x^2+3x-4.`

`:. f(-q/p)=f(-2)=(-2)^4-2(-2)^2+3(-2)-4`

`=16-8-6-4=-2!=0.`

`:. (x+2)" is not a factor of the poly. "f(x).`