Determine the greatest common factor of 24x3y4−15xy2−36x2y3

Answer 1

To determine the greatest common factor of the given expression, we need to find the highest power of each variable that divides all the terms.

First, let's look at the variable x. The highest power of x that appears in all terms is x^1, as it appears as the highest power in the first and second terms and as the second-highest power in the third term.

Next, let's look at the variable y. The highest power of y that appears in all terms is y^2, as it appears as the highest power in the second term and as the second-highest power in the first and third terms.

Now, let's consider the numerical coefficients. We need to find the largest number that divides 24, 15, and 36. The largest number that divides all three is 3.

Putting it all together, the greatest common factor of 24x^3y^4 - 15xy^2 - 36x^2y^3 is 3xy^2.