Determine the greatest common factor of 24x^3y^4-15xy^2-36x^2^y^3. A. 4xy^2. B. xy. C. 3xy^2. D. 3x^2y^2.
To find the greatest common factor (GCF) of 24x^3y^4-15xy^2-36x^2y^3, we need to find the largest expression that divides evenly into all three terms.
First, let's factor each term:
24x^3y^4 = (2^3)*(3)*(x^3)*(y^4)
15xy^2 = (3)*(5)*(x)*(y^2)
36x^2y^3 = (2^2)*(3^2)*(x^2)*(y^3)
Now, let's identify the common factors in all three terms:
The common factor of 2 is 2^1.
The common factor of 3 is 3^1.
The common factor of x is x^1.
The common factor of y is y^1.
Taking the smallest power of each common factor gives us:
GCF = (2^1)*(3^1)*(x^1)*(y^1) = 2*3*x*y = 6xy
Therefore, the greatest common factor of 24x^3y^4-15xy^2-36x^2y^3 is 6xy. The answer is not provided, so it is not one of the options.