3x^3-2x^2-6x+4

Question

i want to know how you can find the greatest common factor of this equation

Answer 1

Try this:

 

Start with

 

3x^3-2x^2-6x+4

 

Combine 1st and second terms, and combine 3rd and 4th terms:

 

(3x^3-2x^2) + (-6x+4)

 

Factor out x^2 from first parenthesis, and factor out 2 from second parenthesis:

 

x^2(3x-2) + 2(-3x+2)

 

Factor out -1 from second parenthesis:

 

x^2(3x-2) - 2(3x-2)

 

Note (3x-2) is common to both terms, so factor it out:

 

(3x-2)(x^2-2)

 

The expression is fully factored now.

 

 

Answer 2

Group the first 2 terms together and the last 2 terms together. In the first 2 terms, factor an x² and a -2 from the last 2 terms. 

 

We have 

 

x²(3x-2) -2(3x-2). 

Now (3x-2) is a common factor in both so we factor it out and it is simplified to

 

(3x-2)(x² -2)