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1 solution
Upon observation, 3 x 3 − 4 x 2 y + 5 x y 2 + 6 y 3 = ( x 2 − 2 x y + 3 y 2 ) ( 3 x + 2 y ) . Since ( x 2 − 2 x y + 3 y 2 ) ∣ ( 3 x 3 − 4 x 2 y + 5 x y 2 + 6 y 3 ) , the remainder is zero.