express f(x) in the form f(x) = (x-k)q(x)+r

Question

f(x)=4x^3+x^2+x-9, k = -1

Answer 1

First divide 4x^3 + x^2 + x - 9 by x + 1 using synthetic division.

-1 l 4 1 1 -9

l -4 3 -4

___________

4 -3 4 -13

So (4x^3 + x^2 + x - 9)/(x + 1) = 4x^2 - 3x + 4 - 13/(x + 1)