# The factor of the expression x 2 − 2 x − 8 . ### 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 97E
To determine

## To calculate: The factor of the expression x2−2x−8 .

Expert Solution

The factor of the expression x22x8 is (x+2)(x4) .

### Explanation of Solution

Given information:

The expression x22x8 .

Formula used:

To find the factor of the trinomial of the form x2+bx+c , find two numbers r and s such that sum of the numbers is equal to coefficient of x (r+s=b) and product of two numbers is equal to constant term (rs=c) , such that (x+r) and (x+s) are the factors of x2+bx+c .

x2+bx+c=x2+(r+s)x+rs=x2+rx+sx+rs=x(x+r)+s(x+r)=(x+r)(x+s)

Calculation:

Consider the given expression x22x8 .

Recall to find the factor of the trinomial of the form x2+bx+c , find two numbers r and s such that sum of the numbers is equal to coefficient of x (r+s=b) and product of two numbers is equal to constant term (rs=c) , such that (x+r) and (x+s) are the factors of x2+bx+c .

x2+bx+c=x2+(r+s)x+rs=x2+rx+sx+rs=x(x+r)+s(x+r)=(x+r)(x+s)

So,find two numbers r and s such that r+s=2 and rs=8 .

So, x22x8 can be written as,

x22x8=x2+(4+2)x+(4)(2)=x24x+2x8=x(x4)+2(x4)=(x+2)(x4)

Thus, the factor of expression x22x8 is (x+2)(x4) .

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