   Chapter 0.6, Problem 11E

Chapter
Section
Textbook Problem

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

To determine

To calculate: The solution of the equation (x+1)3+(x+1)5=0.

Explanation

Given information:

The equation, (x+1)3+(x+1)5=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,

(x+1)3+(x+1)5=0

The left side expression is (x+1)3+(x+1)5.

As both the term contains the term (x+1)3. Thus, the common factor is (x+1)3.

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

(x+1)3+(x+1)5=(x+1)3(1+(x+1)2)=(x+1)3(1+x+1)=(x+2)(x+1)3

Therefore, the factors of the expression (x+1)3+(x+1)5 are (x+2)(x+1)3

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