How do you determine whether x+2 is a factor of the polynomial x^4-2x^2+3x-4x4−2x2+3x−4?

1 Answer
Ratnaker Mehta
Feb 27, 2017

(x+2)" is not a factor of the poly."(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.(px+q) is a Factor of a Poly. f(x)⇔f(−qp)=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.(px+q)=x+2, so that, p=1,q=2, whence, −qp=−2,and,f(x)=x4−2x2+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).

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