Appendix C - Synthetic Division and the Remainder Theorem - C Exercise Set - Page 993: 24

$F(-2)=2$

Using $ -2 $ in operating the coefficients of the given function, $F(x)= 3x^4+8x^3+2x^2-7x-4 ,$ results in the picture shown below. The last row of numbers, $\{ 3,2,-2,-3,2 \},$ represents the coefficients of the quotient and the remainder. Furthermore, the remainder of $\dfrac{f(x)}{x-c}$ is equal to $f(c)$. Hence, $ F(-2)=2 $.