SOLUTION: Write f(x)= x^3+9x^2+15x+58 in the form f(x)=(x-k)q(x)+r when k=-8.

Algebra ->  Rational-functions -> SOLUTION: Write f(x)= x^3+9x^2+15x+58 in the form f(x)=(x-k)q(x)+r when k=-8.      Log On


   

Question 825730: Write f(x)= x^3+9x^2+15x+58 in the form f(x)=(x-k)q(x)+r when k=-8.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
If k = -8 then the desired form is:
f(x)=(x-(-8))q(x)+r
In order to rewrite f(x) in this form, we will use synthetic division to divide f(x) by (x-(-8)):
-8  |  1   9   15   58
-----     -8   -8  -56
      -----------------
       1   1    7    2
The 2 in the lower right corner is the remainder (the "r" in f(x)=(x-k)q(x)+r). The rest of the bottom row is the quotient (the q(x) in f(x)=(x-k)q(x)+r). The "1 1 7" translates into x%5E2%2Bx%2B7. So the answer is:
f%28x%29=%28x-%28-8%29%29%28x%5E2%2Bx%2B7%29%2B2
or
f%28x%29=%28x%2B8%29%28x%5E2%2Bx%2B7%29%2B2

P.S. This is a polynomial, not a rational function. Please post in an appropriate category.