# The common factor of the expression 3 ( 2 x − 1 ) 2 ( 2 ) ( x + 3 ) 1 / 2 + ( 2 x − 1 ) 3 ( 1 2 ) ( x + 3 ) − 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 126E
To determine

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

Expert Solution

The common factor of the expression 3(2x1)2(2)(x+3)1/2+(2x1)3(12)(x+3)1/2 is (2x1)2(x+3)1/2(7x+352) .

### Explanation of Solution

Given information:

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

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

3(2x1)2(2)(x+3)1/2+(2x1)3(12)(x+3)1/2=(2x1)2(x+3)1/2(6(x+3)+(2x1)(12))=(2x1)2(x+3)1/2(6x+18+x12)=(2x1)2(x+3)1/2(7x+1812)=(2x1)2(x+3)1/2(7x+352)

Thus, the common factor of the expression 3(2x1)2(2)(x+3)1/2+(2x1)3(12)(x+3)1/2 is (2x1)2(x+3)1/2(7x+352) .

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