SOLUTION: Factor the following polynomial. {{{18x^2y-24x^2-27y+36}}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Factor the following polynomial. {{{18x^2y-24x^2-27y+36}}}      Log On


   

Question 375417: Factor the following polynomial.
18x%5E2y-24x%5E2-27y%2B36
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Factor the following polynomial.
18x%5E2y-24x%5E2-27y%2B36 
First factor out the common factor 3, using a bracket, so that
parentheses may be placed within:

%223%5B%226x%5E2y-4x%5E2-9y%2B12%22%5D%22


I'll do some coloring for clarity:

%223%5B%22red%286x%5E2y-4x%5E2%29green%28-9y%2B12%29%22%5D%22

Factor red%282x%5E2%2A%22%22%29 out of the two red terms and
factor green%28-3%2A%22%22%29 out of the two green terms

%223%5B%22red%282x%5E2%2A%283y-4%29%29green%28-3%283y-4%29%29%22%5D%22

Now I will recolor the expressions

%223%5B%22green%282x%5E2%29%2Ared%28%283y-4%29%29green%28-3%29red%28%283y-4%29%29%22%5D%22

Factor out the common red factor, and put the two green factors 
as a sum in parentheses:

%223%5B%22red%28%283y-4%29%29green%28%282x%5E2-3%29%29%22%5D%22

The brackets are no longer needed and neither is the special coloring,
so the final answer is:

3%283y-4%29%282x%5E2-3%29

Edwin