Chapter 4.2, Problem 93AYU

To determine

To find: The sum of remaining solutions of $f\left(x\right)=x^3-8x^2+16x-3=0$. one solution $=\text{ 3}$.

Answer to Problem 93AYU

$\text{The sum of the remaining solutions }=(x^2-5x+1)$.

Explanation of Solution

Given:

$f\left(x\right)=x^3-8x^2+16x-3=0$

one solution $=\text{ 3}$.

$\left(x-3\right)$is one of the solutions.

Using synthetic division or long division

$f\left(x\right)=x^3-8x^2+16x-3=0=\left(x-3\right)\left(x^2-5x+1\right)$

The depressed equation $=\left(x^2-5x+1\right)$

The sum of the remaining solutions $=\left(x^2-5x+1\right)$