Question

Use the Factor Theorem to determine whether x+2 is a factor of P(x)=2x^4+x^3-3x-9.


Specifically, evaluate P at the proper value, and then determine whether x+2 is a factor.

P(__)=

x+2 is or is not a factor of P(x)____

Answer 1

The factor theorem states that a polynomial f(x) has a factor (x − k) if and only if f(k) = 0.

So if (x+2) is a factor of P(x), then
P(-2)=0.

Since P(-2)= 21, it is clear that (x+2) is not a factor of P(x)=2x^4+x^3-3x-9.

Answer 2

answer