Chapter 4.2, Problem 94AYU

To determine

To find: The sum of remaining solutions of $f\left(x\right)=x^3+5x^2+5x-2=0$. one solution $=\text{ <mo>−</mo>2}$.

Answer to Problem 94AYU

$\text{The sum of the remaining solutions }=(x^2+3x-1)$.

Explanation of Solution

Given:

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

one solution $=\text{ <mo>−</mo>2}$.

$\left(x-(-2\right))$ is one of the solutions.

Using synthetic division or long division

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

The depressed equation $=\left(x^2+\text{ 3}x-1\right)$

The sum of the remaining solutions $=\left(x^2+\text{ 3}x-1\right)$