Question

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

Answer 1

Given

`P(x)=x^3+4x^2-8`

To determine whether (x+2) is a factor of P(x), we find the value of P(-2). If P(-2)=0, then by factor theorem, we can say that (x+2) is a factor of P(x).

`\begin{gathered} P(-2)=(-2)^3+4(-2)^2-8 \\ =-8+16-8 \\ =-16+16 \\ =0 \end{gathered}`

Hence (x+2) is a factor of P(x).