(2x^3 - 5x^2y + 5xy^2 - 3y^3) ÷ (2x - 3y) =?
- x^2 - xy + y^2
- x^2 - xy + 3y^2
- x^2 - xy + 2y^2
- None of these
Explanation
To divide (2x^3 - 5x^2y + 5xy^2 - 3y^3) by (2x - 3y), let's attempt polynomial long division or factorization if possible.
Given the form of the dividend and divisor, let's try to factor or directly apply division:
(2x^3 - 5x^2y + 5xy^2 - 3y^3) ÷ (2x - 3y)
Upon inspection or performing polynomial division, one notices:
2x^3 - 5x^2y + 5xy^2 - 3y^3 can be factored or divided as follows:
2x^3 - 3x^2y - 2x^2y + 3xy^2 + 2xy^2 - 3y^3
Which can be rearranged and factored:
x^2(2x - 3y) - xy(2x - 3y) + y^2(2x - 3y)
= (2x - 3y)(x^2 - xy + y^2)
Thus, (2x^3 - 5x^2y + 5xy^2 - 3y^3) ÷ (2x - 3y) = x^2 - xy + y^2
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