   Chapter 0.6, Problem 8E

Chapter
Section
Textbook Problem

Solve the equations in Exercises 1–26. 10 x ( x 2 + 1 ) 4 ( x 3 + 1 ) 5 − 10 x 2 ( x 2 + 1 ) 5 ( x 3 + 1 ) 4 = 0

To determine

To calculate: The solution of the equation 10x(x2+1)4(x3+1)510x2(x2+1)5(x3+1)4=0.

Explanation

Given information:

The equation, 10x(x2+1)4(x3+1)510x2(x2+1)5(x3+1)4=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,

10x(x2+1)4(x3+1)510x2(x2+1)5(x3+1)4=0

The left side expression is 10x(x2+1)4(x3+1)510x2(x2+1)5(x3+1)4.

As both the term contains the term 10x(x2+1)4(x3+1)4. Thus, the common factor is 10x(x2+1)4(x3+1)4.

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

10x(x2+1)4(x3+1)510x2(x2+1)5(x3+1)4=10x(x2+1)4(x3+1)4(x3+1x(x2+1))=10x(x2+1)4(x3+1)4(x3+1x3x)=10x(x2+1)4(x3+1)4(1x)

Therefore, the factors of the expression 10x(x2+1)4(x3+1)510x2(x2+1)5(x3+1)4 are 10x(x2+1)4(x3+1)4(1x)

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