factor the following problem

Question

1/3 x^2 -1/9 x

Answer 1

Consider the following example:

 

(1/a) b² + (1/(ac)) b

 

Ask what is the common factors?

 

(1/a) and (1/(ac)) have a common factor of  (1/a):

 

(1/a)(b²+(1/c)b)

 

b² and b have a common factor of b:

 

(1/a) b(b + (1/c))

 

Thus the factors are (1/a)b and (b+(1/c)).

 

With numbers:

 

(1/2)x³-(1/6)x²

 

1/2 and 1/6 have a common factor of 1/2:

 

(1/2)(x³-(1/3)x²)

 

x³ and x² have a common factor of x²:

 

(1/2)x²(x-(1/3))

 

Thus, the common factors are (1/2)x² and (x-(1/3))

 

So in your problem you should be asking:

What are the common factors of (1/3) and (1/9)?

What are the common factors of x² and x?

Answer 2

x²/3 - x/9

3x²/9 - x/9                      LCD

(x/9)(3x² - 1)                  GCF

(x/9)(x√3 + 1)(x√3 - 1)  Difference of squares