Question

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

Answer 1

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