Appendix C - Synthetic Division and the Remainder Theorem - C Exercise Set - Page 993: 25

$f(4)=0$

Using $ 4 $ in operating the coefficients of the given function, $f(x)= x^4-6x^3+11x^2-17x+20 ,$ results in the picture shown below. The last row of numbers, $\{ 1,-2,3,-5,0 \},$ represents the coefficients of the quotient and the remainder. Furthermore, the remainder of $\dfrac{f(x)}{x-c}$ is equal to $f(c)$. Hence, $ f(4)=0 $.