John R. answered 01/15/13
John R: Math, Science, and History Teacher
I am going to use the following for the example for all statement below:
4x4y - 6x3yz + 8x2y2
Begin by finding common factors among the constants in front. Looking at the example, the constants 4, 6, & 8 have a common factor of 2.
After finding in common constants, look for common variables. In the example, x and y occur in all three terms. Once the common variables are identified, find the lowest exponent on each. In the example, the lowest exponent on x is 2 and the lowest exponent on y is 1. Therefore, x2 and y1 can be factored out (the 1 on y is only written for example and would not appear in the answer).
Just as you would divide each term by 2 when factoring out the 2, you need to divide each term by x2y when factoring out the x2y.
After factoring, the example would appear as:
2x2y(2x2 - 3xz + 4y)