   Chapter 0.3, Problem 28E

Chapter
Section
Textbook Problem

In Exercises 23–30, factor each expression and simplify as much as possible. ( x 2 + 1 ) x + 1 − ( x + 1 ) 3

To determine

To calculate: The factors of the expression (x2+1)x+1(x+1)3 and write it in the simplest form.

Explanation

Given information:

The expression, (x2+1)x+1(x+1)3.

Formula used:

Steps to calculate the factors,

Step1: Factor out the common factor.

Step2: Simplify the remaining terms.

Calculation:

Consider the expression,

(x2+1)x+1(x+1)3

Rewrite the above expression as below,

(x2+1)x+1(x+1)2x+1

As both the term contains the term x+1. Thus, the common factor is x+1.

Now, factor out the common factor and simplify as below,

(x2+1)x+1(x+1)3=x+1(x2+1(x+1)2)

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