# The factor of the expression ( x − 1 ) ( x + 2 ) − 2 ( x − 1 ) 2 ( x + 2 ) .

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.3, Problem 121E
To determine

## To calculate: The factor of the expression (x−1)(x+2)−2(x−1)2(x+2) .

Expert Solution

The factor of the expression (x1)(x+2)2(x1)2(x+2) is 3(x1)(x+2) .

### Explanation of Solution

Given information:

The expression (x1)(x+2)2(x1)2(x+2) .

Formula used:

To factor out the common factor from a polynomial, find out the greatest common factor and express the polynomial as a product of the simpler ones.

Calculation:

Consider the given expression (x1)(x+2)2(x1)2(x+2) .

Recall that to factor out the common factor from a polynomial, find out the greatest common factor and express the polynomial as a product of the simpler ones.

The common factor of these terms is (x1)(x+2) .

Simplify (x1)(x+2)2(x1)2(x+2) further as,

(x1)(x+2)2(x1)2(x+2)=(x1)(x+2)[(x+2)(x1)]=(x1)(x+2)(x+2x+1)=(x1)(x+2)(3)=3(x1)(x+2)

Thus, the factor of expression (x1)(x+2)2(x1)2(x+2) is 3(x1)(x+2) .

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