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 1.3, Problem 68E
To determine

To calculate: The factors of the trinomial x26x+5 .

Expert Solution

Answer to Problem 68E

The factors of the trinomial x26x+5 are x5 and x1 .

Explanation of Solution

Given information:

The expression x26x+5 .

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 x26x+5 .

Recall that 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=6 and rs=5 .

Here, r=5 and s=1 , so, x26x+5 will be factorized as,

  x26x+5=x2+(51)x+(5)(1)=x25xx+5=x(x5)1(x5)=(x5)(x1)

Thus, the factors of trinomial x26x+5 are x5 and x1 .

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!