Is x+1x+1 a factor of x^3+8x^2+11x-20x3+8x2+11x20?

1 Answer
Nov 8, 2016

(x+1)(x+1) is not a factor, but (x-1)(x1) is.

Explanation:

Given p(x)=x^3+8x^2+11x-20p(x)=x3+8x2+11x20 if x+1x+1 is a factor of p(x)p(x) then

p(x)=(x+1)q(x)p(x)=(x+1)q(x) so for x=-1x=1 we must have

p(-1)=0p(1)=0

Verifying on p(x)p(x)

p(-1)=(-1)^3+8(-1)^2+11(-1)-20=-24p(1)=(1)3+8(1)2+11(1)20=24

so (x+1)(x+1) is not a factor of p(x)p(x)

but (x-1)(x1) is a factor because

p(1)=1+8+11-20=0p(1)=1+8+1120=0