Determine the greatest common factor of
24x^3y^4-15xy^2-36x^2^y^3
Answers
4xy^2
xy
3xy^2
3X^2y^2
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".