   Chapter 0.6, Problem 6E

Chapter
Section
Textbook Problem

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

To determine

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

Explanation

Given information:

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

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

As both the term contains the term (x+1)(x+2). Thus, the common factor is (x+1)(x+2).

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

(x+1)(x+2)2+(x+1)2(x+2)=(x+1)(x+2){(x+2)+(x+1)}=(x+1)(x+2)(2x+3)

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

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