Chapter 5 Polynomials and Polynomial Functions - 5.4 Factor and Solve Polynomial Equations - 5.4 Exercises - Mixed Review - Page 359: 77

See below

We are given: $f(x)=-3x^5+x^3-6x^2+2x+4$ where $x=-4$ Rewrite as: $f(x)=(x+3)q(x)+r(x)$ Since the degree must be smaller than that of $x+3$, $r(x)$ has a degree of $0$. Substitute $-3$ for $x$: $f(-3)=(-3+3)q(x)+r\\ \rightarrow f(-3)=r$ We can see that $f(-3)=646$