# To simplify x 2 − 2 x − 3 2 x 2 + 5 x + 3 by using appropriate operations.

### 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, Problem 54RE
To determine

## To simplify x2−2x−32x2+5x+3 by using appropriate operations.

Expert Solution

### Explanation of Solution

Given information:

x22x32x2+5x+3

Formula used:

Factoring Trinomials:- To factor the form x2+bx+c

(x+r)(x+s)=x2(r+s)x+rs where r+s=b and rs=c .

Calculations:

By factoring both numerator and denominator we get,

Numerator = x22x3

where r=3 and s=1 .

r+s=3+1=2rs=(3)(1)=3(x+r)(x+s)=(x3)(x+1)  (i)

Denominator = 2x2+5x+3

where r=2 and s=3 .

r+s=2+3=5rs=(3)(2)=6(x+r)(x+s)=(x+2)(x+3)  (ii)

Now, dividing equation (i) and (ii) we get,

=(x3)(x+1)(x+2)(x+3)

After simplifying we get (x3)(x+1)(x+2)(x+3) .

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