Question

Write f(x)=x^3+8x^2+13x+33 in the form f(x)=(x-k)q(x)+r when k=-7.

Answer 1

Either perform a long algebraic division of x^3 + 8x^2 + 13x + 33 by (x+7) or do synthetic division.

I will attempt to line up the synthetic division, hopefully the spacing looks ok

-7 | 1 8 13 33
.... -7 -7 -42
.... 1 1 6 -9

so x^3+8x^2+13x+33 = (x+7)(x^2 + x + 6) - 9