What is the remainder when f(x) = x4− 8x2 + 10x + 22 is divided by x + 3?

Question

divide x4-8x2+10x+22 by x+3

Answer 1

one is the remainder, 1.

x+3 divides the 4th degree polynomial

(x^4 -8x^2+10x +22)/(x+3) = x^3-3x^2+x+7 +1/(x+3)

Had the polynomial ended with a constant term of 21 instead of 22, the division would have had a zero remainder.

Use either synthetic or long division