Explanation

Step 1: Perform polynomial long division or synthetic division

To find the quotient when (2x³ - 5x²y + 5xy² - 3y³) is divided by (2x - 3y), let's try factoring or direct division.

Step 2: Factor the numerator if possible

Notice that (2x³ - 5x²y + 5xy² - 3y³) can be factored as:

(2x³ - 3x²y) + (-2x²y + 3xy²) + (2xy² - 3y³)

= x²(2x - 3y) - xy(2x - 3y) + y²(2x - 3y)

= (2x - 3y)(x² - xy + y²)

Step 3: Identify the quotient

Given the factorization (2x - 3y)(x² - xy + y²), the quotient when (2x³ - 5x²y + 5xy² - 3y³) is divided by (2x - 3y) is x² - xy + y².