Question

Write the function in the form
f(x) = (x − k)q(x) + r
for the given value of k.
f(x) = x^3 − 6x^2 − 13x + 9, k = −2

Answer 1

my answer was (x+2)(x^2-8x+3)-3 but it was wrong.

Answer 2

(x+2)(x^2-8x+3)+3
plus instead of the minus

Answer 3

thanks! but i don't understand though.

Answer 4

x^3 − 6x^2 − 13x + 9 = x^3 − 6x^2 − 13x +6 +3

(x^3 − 6x^2 − 13x +6)/(x+2) = (x^2-8x+3)

so (x^3 − 6x^2 − 13x +6) = (x+2)(x^2-8x+3)
thus
x^3 − 6x^2 − 13x + 9 = x^3 − 6x^2 − 13x +6 +3
= (x+2)(x^2-8x+3) +3