Is x+2 a factor of p(x)=x^4+3x^3+4x^2-8? Why?

1 Answer
Jan 21, 2017

Yes it is a factor

Explanation:

The factor theorem states that:

Given a polynomial P(x), (x-a) is a factor of P(x) if and only if P(a) = 0

So from the question, we are given that P(x) = x^4 + 3x^3 + 4x^2 -8 and the factor we're testing is (x+2) which can be written as (x-(-2)). From this we can apply the factor theorem:

P(-2) = (-2)^4+3(-2)^3+4(-2)^2-8
= 0

Hence (x-2) is a factor of P(x) and we're done