Question

Use the remainder theorem to find P(-2) for P(x) = x³ + 2x² +6. Specifically, give the quotient and the remainder for the associated division and the value of P(-2).

Answer 1

$\begin{gathered} p(x)=x^3+2x^2+6 \\ x=-2 \\ -2^3+2(-2)^2+6 \\ -8+8+6 \\ 6\text{ is the remainder} \\ \end{gathered}$$\frac{(x^3+2x^2+6)}{x+2}=x^2+\frac{6}{x+2}\text{ this is the quotient}$$\text{ the value of p\lparen-2\rparen is 6}$