   Chapter 0.6, Problem 5E

Chapter
Section
Textbook Problem

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

To determine

To calculate: The solution of the equation (x+1)(x+2)+(x+1)(x+3)=0.

Explanation

Given information:

The equation, (x+1)(x+2)+(x+1)(x+3)=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)+(x+1)(x+3)=0

The left side expression is (x+1)(x+2)+(x+1)(x+3).

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,

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

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

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