Use the Factor Theorem to determine whether x+2 is a factor of P(x)=x^4+x^3-5x^2+ 7. Specifically, evaluate P at the proper value, and then determine whether x+2 is a factor.

Answer 1

By factor theorem if P(- 2) = 16 - 8 - 20 + 7 ≠ 0 then (x + 2) not a factor of P(x)

Answer 2

If x+2 is a factor then P(-2)=0 .

Find P(-2)= (-2)^4 +(-2)^3 -5((-2)^2)+7 = 16-8-10+7 = -5

Therefore x+2 is not a factor