jmc

Using the Remainder Theorem, the remainder when $f(x)=x^4-7x^3+9x^2+16x-13$ is divided by $x-3$ is $$\begin{array}{rl}f(3)& =3^4-7\cdot 3^3+9\cdot 3^2+16\cdot 3-13\\ & =3^3(3-7+3)+35\\ & =\boxed{8}.\end{array}$$