# The common factor of the expression 5 ( x 2 + 4 ) 4 ( 2 x ) ( x − 2 ) 4 + ( x 2 + 4 ) 5 ( 4 ) ( x − 2 ) 3 .

### 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 125E
To determine

## To calculate: The common factor of the expression 5(x2+4)4(2x)(x−2)4+(x2+4)5(4)(x−2)3 .

Expert Solution

The common factor of the expression 5(x2+4)4(2x)(x2)4+(x2+4)5(4)(x2)3 is 2(x2+4)4(x2)3(7x210x+8) .

### Explanation of Solution

Given information:

The expression 5(x2+4)4(2x)(x2)4+(x2+4)5(4)(x2)3 .

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 5(x2+4)4(2x)(x2)4+(x2+4)5(4)(x2)3 .

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 2(x2+4)4(x2)3 .

So, 5(x2+4)4(2x)(x2)4+(x2+4)5(4)(x2)3 can be written in simplified form as,

5(x2+4)4(2x)(x2)4+(x2+4)5(4)(x2)3=2(x2+4)4(x2)3(5x(x2)+2(x2+4))=2(x2+4)4(x2)3(5x210x+2x2+8)=2(x2+4)4(x2)3(7x210x+8)

Thus, the common factor of the expression 5(x2+4)4(2x)(x2)4+(x2+4)5(4)(x2)3 is 2(x2+4)4(x2)3(7x210x+8) .

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