PLEASE HELP! I need to write the function in the form: f(x)=(x-k)q(x)+r(x) for the given value of k and use a graphing utility to demonstrate that f(k)=r.

The function is f(x)=15x^4+10x^3-6x^2+14 and the value of k is k=-2/3.

Where do I even begin???

Question

PLEASE HELP! I need to write the function in the form: f(x)=(x-k)q(x)+r(x) for the given value of k and use a graphing utility to demonstrate that f(k)=r.

The function is f(x)=15x^4+10x^3-6x^2+14 and the value of k is k=-2/3. 

Where do I even begin???

anonymous · Answer

@jdoe0001 do you think you could help me out with this? I don't understand it at all!

jdoe0001 · Answer

well.. .I know what's asking for.... $\large \begin{array}{llll}
f(x)=&(x-k)&q(x)+&r(x)\
&\quad \uparrow&\uparrow &\uparrow  \
&binomial&quotient&remainder
\end{array}$

meaning.... find a binomial, that multiplied by a quotient and adding a remainder, gives us f(x)

so say  $\bf \cfrac{15x^4+10x^3-6x^2+14}{x-k}\implies 15x^4+10x^3-6x^2+14\div (x-k)$

so that division will give  you some quotient, and a remainder
so working in REVERSE, you'd multiply the quotient, times the binomial and add the remainder

jdoe0001 · Answer

I guess, a quick example of that will be |dw:1389475997930:dw|