The remainder theorem lets us find the remainder when a polynomial f(x) is divided by a linear factor (g(x))
Given f(x)=x^4+x^3-3x-3
Need to find the remainder when f(x) is divided by g(x)=x+2.
The zero of can be found by g(x)=0=x+2 => x=-2
The remainder is then f(-2)=(-2)^4+(-2)^3-3(-2)-3=16-8+6-3=11