Chapter 8.5, Problem 5MRE

To determine

To calculate the value of the expression.

Answer to Problem 5MRE

The value of the expression $\frac{a^5-4a^3+3a}{a+1}$ is $a^4-a^3-3a^2+3a$

Explanation of Solution

Given information: Consider the given expression,

  $\frac{a^5-4a^3+3a}{a+1}$

Calculation : the following expression is simplified as:

  $\frac{a^5-4a^3+3a}{a+1}$

Using long division,

  $a+1\begin{array}{c}\hfill a^4-a^3-3a^2+3a\\ \hfill \overline{)a^5-4a^3+3a}\end{array}$

  $-a^5+a^4$

  $-a^4-4a^3$

  $-a^4-a^3$

  $-3a^3+3a$

  $-3a^3-3a^2$

  $3a^2+3a$

  $-3a^2+3a$

  0

Hence,

The value of the expression $\frac{a^5-4a^3+3a}{a+1}$ is $a^4-a^3-3a^2+3a$