Question

Which of the following is the result of using the remainder theorem to find F(-2) for the polynomial function F(x) = -2x³ + x² + 4x-3?

Answer 1

We have the polynomial

`f(x)=-2x^3+x^2+4x-3`

Usin the remainder theorem, we find f(-2) by substituting x = -2

So we have

`\begin{gathered} f(x)=-2x^(3)+x^(2)+4x-3 \\ \\ f(-2)=-2(-2)^3+(-2)^2+4(-2)-3 \\ \\ f(-2)=-2(-8)+4-8-3 \\ \\ f(-2)=16+4-8-3 \\ \\ f(-2)=20-11 \\ \\ f(-2)=9 \end{gathered}`

Therefore, the remainder is

`9`