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Polynomial Division problems

Open solved problems with answers and gated step-by-step solutions.

What is the remainder when (3x^3 - 2x^2 + 4x - 3) is divided by (x^2 + 3x + 3)?

What is the quotient of (x^3 + 8) divided by (x + 2)?

What is the quotient of (x^3 + 6x^2 + 11x + 6) divided by (x^2 + 4x + 3)?

What is the quotient of (x^3 + 3x^2 + 5x + 3) divided by (x + 1)?

What is the remainder of the following division problem?

What is the quotient of (x^3 - 3x^2 + 5x - 3) divided by (x - 1)?