Appendix C - Synthetic Division and the Remainder Theorem - C Exercise Set - Page 993: 21

$f(-3)=6$.

By synthetic division, using $ -3 $ in operating the coefficients of the given function, $f(x)= 5x^4+12x^3+28x+9 ,$ results to the picture shown below. The last row of numbers, $\{ 5,-3,9,1,6 \},$ represent the coefficients of the quotient and the remainder. Furthermore, the remainder of $\dfrac{f(x)}{x-c}$ is equal to $f(c)$. Hence, $f(-3)=6$.