Question

Find the remainder when f(x) = 5x^3 + 7x + 5 is divided by x + 2.

Answer 1

If you divide f(x) by x+2, you will get a quotient and a remainder, which I will call q(x) and r(x). So\[f(x)=q(x)(x+2)+r(x)\]Plug in x=-2 and we get:\[f(-2)=q(-2)(-2+2)+r(-2)\Longrightarrow f(-2)=q(-2)\cdot0+r(-2)\]\[=r(-2)\]So, in short, evauate the function at -2. that will be the remainder when you divide that polynomial by x+2.