# The factor of the expression 3 x − 1 2 + 4 x 1 2 + x 3 2 .

### 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 1.3, Problem 90E
To determine

## To calculate: The factor of the expression 3x−12+4x12+x32 .

Expert Solution

The factor of the expression 3x12+4x12+x32 is 1x(x+1)(x+3) .

### Explanation of Solution

Given information:

The expression 3x12+4x12+x32 .

Formula used:

To factor an expression, split the terms in the expression into multiplication of simpler expressions, then take the common power out and group the expressions together.

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 3x12+4x12+x32 .

Recall that to factor an expression, split the terms in the expression into multiplication of simpler expressions, then take the common power out and group the expressions together.

The greatest common factor of these terms is x12 .

Apply it,

3x12+4x12+x32=x12(3+4x12x12+x32x12)=x12(3+4x12(12)+x32(12))=1x(3+4x+x2)=1x(x2+4x+3)

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, 1x(x2+4x+3) will be further simplified as,

3x12+4x12+x32=1x(x2+4x+3)=1x(x2+3x+x+3)=1x[x(x+3)+1(x+3)]=1x(x+1)(x+3)

Thus, the factor of expression 3x12+4x12+x32 is 1x(x+1)(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!