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 98E
To determine

To calculate: The factor of the expression x214x+48 .

Expert Solution

Answer to Problem 98E

The factor of the expression x214x+48 is (x8)(x6) .

Explanation of Solution

Given information:

The expression x214x+48 .

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 x214x+48 .

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=14 and rs=48 .

So, x214x+48 can be written as,

  x214x+48=x2+(68)x+(6)(8)=x26x8x+48=x(x6)8(x6)=(x8)(x6)

Thus, the factor of expression x214x+48 is (x8)(x6) .

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