BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1, Problem 54RE
To determine

To simplify x22x32x2+5x+3 by using appropriate operations.

Expert Solution

Answer to Problem 54RE

The answer is (x3)(x+1)(x+2)(x+3) .

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) .

Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!