   Chapter 0.6, Problem 9E

Chapter
Section
Textbook Problem

Solve the equations in Exercises 1–26. ( x 3 + 1 ) x + 1 − ( x 3 + 1 ) 2 x + 1 = 0

To determine

To calculate: The solution of the equation (x3+1)x+1(x3+1)2x+1=0.

Explanation

Given information:

The equation, (x3+1)x+1(x3+1)2x+1=0.

Formula used:

Zero product property,

If a product of two number is zero, one of the two must be zero.

Calculation:

Consider the expression,

(x3+1)x+1(x3+1)2x+1=0

The left side expression is (x3+1)x+1(x3+1)2x+1.

As both the term contains the term (x3+1)x+1. Thus, the common factor is (x3+1)x+1.

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

(x3+1)x+1(x3+1)2x+1=(x3+1)x+1(1x3+1)=(x3+1)x+1(x3)=x3(x3+1)x+1

Therefore, the factors of the expression (x3+1)x+1(x3+1)2x+1 are x3(x3+1)x+1

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