Question 825730
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)):
<pre>
-8  |  1   9   15   58
-----     -8   -8  -56
      -----------------
       1   1    7    2
</pre>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^2+x+7}}}. So the answer is:
{{{f(x)=(x-(-8))(x^2+x+7)+2}}}
or
{{{f(x)=(x+8)(x^2+x+7)+2}}}<br>
P.S. This is a polynomial, <u>not</u> a rational function. Please post in an appropriate category.