Determine the greatest common factor of

24x^3y^4-15xy^2-36x^2^y^3

Answers
4xy^2
xy
3xy^2
3X^2y^2

1 answer

To find the greatest common factor (GCF), we need to find the highest power of each variable that appears in all of the terms.

The variables in the expression are x and y. Let's look at the powers of x first:
- 24x^3y^4 has x raised to the power of 3.
- 15xy^2 has x raised to the power of 1.
- 36x^2y^3 has x raised to the power of 2.

The highest power of x that appears in all of the terms is 1 (x^1).

Now let's look at the powers of y:
- 24x^3y^4 has y raised to the power of 4.
- 15xy^2 has y raised to the power of 2.
- 36x^2y^3 has y raised to the power of 3.

The highest power of y that appears in all of the terms is 2 (y^2).

Therefore, the GCF is xy^2. So, the correct answer is "xy".