What is the greatest common factor of a polynomial? How do you know when you have found the greatest one? Explain your answers, show a demonstration and give a problem for the class to try.

To find the greatest common factor of a polynomial is rather simple. You have to break down each term of the polynomial to its basic factored out pieces. In the following equation I will show you how to find the greatest common factor of the polynomial. 10x^2y^2+ 5xy+20y. In this equation the highest common factor is 5. You must now identify the highest common variable between all elements of the polynomial. In this equation the highest common factor is just y so our new greatest common factor is 5y. When we factor this out of our polynomial we get 5y(2x^2y + x + 4x). An example for the class to try is: 15x^3y^2 -3x^2y^2+15y^2