Appendix C - Synthetic Division and the Remainder Theorem - C Exercise Set - Page 993: 22

$g(3)=0$

Using $ 3 $ in operating the coefficients of the given function, $g(x)= 3x^4-25x^2-18 ,$ results in the picture shown below. The last row of numbers, $\{ 3,9,2,6,0 \},$ represents the coefficients of the quotient and the remainder. Furthermore, the remainder of $\dfrac{f(x)}{x-c}$ is equal to $f(c)$. Hence, $ g(3)=0 $.