In Exercises 37 42, write the function in the form f(x) = (x k)q(x) + r(x) for the given

Chapter 3, Problem 42

(choose chapter or problem)

Verifying the Remainder Theorem

In Exercises 37– 42, write the function in the form \(f(x)=(x-k)q(x)+r(x)\) for the given value of k. Use a graphing utility to demonstrate that \(f(k)=r\).

                    Function                                        Value of k

\(f(x)=-3 x^{3}+8 x^{2}+10 x-8\)                    \(k=2+\sqrt{2}\)

Text Transcription:

f(x)=(x-k)q(x)+r(x)

f(k)=r

f(x)=-3x^{3}+8x^{2}+10x-8

k=2+sqrt{2}