What is the remainder when (3x3 – 2x2 + 4x – 3) is divided by (x2 + 3x + 3)?

When dividing by x² + 3x + 3, use x² = −3x − 3. This gives x³ = x(−3x − 3) = 6x + 9. Substituting into 3x³ − 2x² + 4x − 3 gives 3(6x + 9) − 2(−3x − 3) + 4x − 3 = 28x + 30, so the remainder is 28x + 30.

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