Determine the greatest common factor of 24x3y4−15xy2−36x2y3%0D%0A24%0D%0A%0D%0A3%0D%0A%0D%0A4%0D%0A−%0D%0A15%0D%0A%0D%0A%0D%0A2%0D%0A−%0D%0A36%0D%0A%0D%0A2%0D%0A%0D%0A3%0D%0A :

Answer 1

To find the greatest common factor of the given expression, we need to factor each term and find the common factors.

Factoring the expression:
24x^3y^4 - 15xy^2 - 36x^2y^3 can be rewritten as:
3xy^2(8x^2y^2 - 5 - 12xy).

Now, let's find the factors of all the numbers in all the terms:
24: 2 * 2 * 2 * 3
3: 3
4: 2 * 2
15: 3 * 5
2: 2
36: 2 * 2 * 3

Now, let's find the common factors of all the terms:
The greatest common factor (GCF) is found by multiplying the common factors with the lowest exponent.

The factors of 24x^3y^4 are 2, 2, 2, 3, x, x, x, y, y, y, y.
The factors of 15xy^2 are 3, x, y, y.
The factors of 36x^2y^3 are 2, 2, 3, x, x, y, y, y.

Common factors are: 2, 3, x, x, y, y, y.

Therefore, the greatest common factor (GCF) is 2 * 3 * x * x * y * y * y, which simplifies to:
6x^2y^3.