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Mathematics
OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (hoblos):

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

OpenStudy (anonymous):

thanks! but i don't understand though.

OpenStudy (hoblos):

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

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