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 67E
To determine

To calculate: The factors of the trinomial x2+2x3 .

Expert Solution

Answer to Problem 67E

The factors of the trinomial x2+2x3 are x+3 and x1 .

Explanation of Solution

Given information:

The expression x2+2x3 .

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 x2+2x3 .

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=2 and rs=3 .

Here, r=3 and s=1 , so, x2+2x3 will be factorized as,

  x2+2x3=x2+(31)x+(3)(1)=x2+3xx3=x(x+3)1(x+3)=(x+3)(x1)

Thus, the factors of trinomial x2+2x3 are x+3 and x1 .

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