1. ## Pre-Calculus Expressing function

Hey, I am having trouble understanding how to figure this problem out. Any help is appreciated.

Express 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(x) = r(x)
Function: f(x) = 15x^4 + 10x^3 - 6x^2 + 14
Value of k: -2/3

2. Originally Posted by tsmith
Hey, I am having trouble understanding how to figure this problem out. Any help is appreciated.

Express 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(x) = r(x).

Check this equation.

Function: f(x) = 15x^4 + 10x^3 - 6x^2 + 14
Value of k: -2/3

use synthetic division ...

Code:
-2/3]..15.....10....-6......0.....14
.............-10.....0......4....-8/3
---------------------------------------
......15.....0.....-6......4....34/3
$\displaystyle \left(x + \frac{2}{3}\right)(15x^3 - 6x + 4) + \frac{34}{3x+2}$

3. ## Thank you

Thanks for the help. I understand it now.