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