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 90E
To determine

To calculate: The factor of the expression 3x12+4x12+x32 .

Expert Solution

Answer to Problem 90E

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) .

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