Part A: Divide (16x^5y^4 + 6x^3y - 2x^2y - 24x^2y^4) by -2x^2y.

Part B: How would your answer in Part A be affected if the x2 variable in the denominator was just an x?

Part C: What is the degree and classification of the polynomial you got in Part A?

Is this first part right?
(x^2 y (16 x^5 y^4+6 x^3 y-2 x^2 y-24 x^2 y^4))/(-2)
Factor (2 x^2 y (8 x^3 y^3+3 x-1-12 y^3) x^2 y)/(-2)
(2 x^2 y (8 x^3 y^3+3 x-1-12 y^3) x^2 y)/(-2).
Add powers together (2^1-1 x^2+2 y^1+1 (8 x^3 y^3+3 x-1-12 y^3))/(-1)
simplify
-x^4 y^2 (8 x^3 y^3+3 x-1-12 y^3)

16x^5y^4 + 6x^3y - 2x^2y - 24x^2y^4

= 2x^2y (8x^3y^3 + 3x - 1 - 12y^3)
= -2x^2y (-8x^3y^3 - 3x + 1 + 12y^3)

Naturally, if the divisor had only an x instead of x^2, all the terms in the quotient would have an extra x in them.

12y^3 + 1 - 3x - 8x^3y^3 is of degree 6, with integer coefficients

Part A: To divide (16x^5y^4 + 6x^3y - 2x^2y - 24x^2y^4) by -2x^2y, you can use long division or synthetic division.

Long Division method:
1. Write the dividend (16x^5y^4 + 6x^3y - 2x^2y - 24x^2y^4) inside the division symbol.
2. Write the divisor (-2x^2y) outside the division symbol.
3. Divide the first term of the dividend (16x^5y^4) by the first term of the divisor (-2x^2y). The result is -8x^3y^3.
4. Multiply the divisor (-2x^2y) by -8x^3y^3. The result is 16x^5y^4.
5. Subtract the product (16x^5y^4) from the first term of the dividend (16x^5y^4). The result is 0.
6. Bring down the next term of the dividend (6x^3y).
7. Repeat steps 3 to 6 until all terms have been divided.
8. The quotient is obtained by adding all the division results: -8x^3y^3.

Synthetic Division method:
1. Write the coefficients of the dividend (16, 0, -2, -24) in order of descending exponents.
2. Write the coefficients of the divisor (-2, 0, 0, 0) in order of descending exponents.
3. Perform synthetic division by dividing each term of the dividend by the first term of the divisor.
4. The result of synthetic division is (-8, 0, 3, -1). This represents the quotient (-8x^3y^3 + 0x^2y^2 + 3xy - 1).

So, the result of dividing (16x^5y^4 + 6x^3y - 2x^2y - 24x^2y^4) by -2x^2y is -8x^3y^3.

Part B: If the x^2 variable in the denominator was changed to just an x, the division process would be affected. The quotient would contain terms with different exponents and the result would be different than in the original case. The new division would involve dividing each term by -2xy instead of -2x^2y.

Part C: The polynomial obtained in Part A after division is -8x^3y^3. The degree of this polynomial is 3 since it is the highest exponent of x or y in any term. The classification of this polynomial is a cubic polynomial with respect to x.