10x^2y^2+15xy^3-5xy^2

Question

How would I find the greatest common factor of this problem? I dont nessesarily care about the answer as much as the steps to solve it, I have it for a homework question and was never taught how to do this.

Answer 1

Take a look at the constants first. Each is a multiple of 5, so 5 is a factor and we can write:

5(2x²y²+3xy³-xy²).

Now the contents of the parentheses. xy² is a common factor because the lowest power of x is 1, making x a factor; and the lowest power of y is 2, making y² a factor, so we combine x with y² to get factor xy², which joins 5 outside the parentheses:

5xy²(2x+3y-1), when we reduce the powers of x by 1 and y by 2. So the HCF is 5xy². It’s the highest common factor because it combines all the other common factors into one.