# The common factor of the expression 1 2 x − 1 / 2 ( 3 x + 4 ) 1 / 2 − 3 2 x 1 / 2 ( 3 x + 4 ) − 1 / 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 128E
To determine

## To calculate: The common factor of the expression 12x−1/2(3x+4)1/2−32x1/2(3x+4)−1/2 .

Expert Solution

The common factor of the expression 12x1/2(3x+4)1/232x1/2(3x+4)1/2 is 2x1/2(3x+4)1/2 .

### Explanation of Solution

Given information:

The expression 12x1/2(3x+4)1/232x1/2(3x+4)1/2 .

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 12x1/2(3x+4)1/232x1/2(3x+4)1/2 .

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.

Here, the terms have the common factor 12x1/2(3x+4)1/2 .

So, 12x1/2(3x+4)1/232x1/2(3x+4)1/2 can be written in simplified form as,

12x1/2(3x+4)1/232x1/2(3x+4)1/2=12x1/2(3x+4)1/2[(3x+4)1/2(3x+4)1/23(x1/2x1/2)]=12x1/2(3x+4)1/2(3x+43x)=12x1/2(3x+4)1/2(4)=2x1/2(3x+4)1/2

Thus, the common factor of the expression 12x1/2(3x+4)1/232x1/2(3x+4)1/2 is 2x1/2(3x+4)1/2 .

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