Use the Factor Theorem to determine whether x+2 is a factor of P(x) = -x^4 -2x^3 + 6x^2 - 24. Specifically, evaluate P at the proper value, and then determine whether x+2 is a factor.

Question

P(?)=?

Is x+2 a factor of P(x)

Is x+2 not a factor of P(x)

Answer 1

P(x)=-x^4 -2x^3+6x^2-24

replace x by -2

P(-2) =-(-2)^4 -2(-2)^3+6(-2)^2 -24

= -16 +16 +24 -24 = 0

P(-2) = 0

x+2 is a factor

x+2 =0

x =-2 is a zero, root, an x intercept when the 4th degree polynomial is graphed

divide the 4th degree polynomial by x+2 and the quotient is another factor, -x^3+6x -12