What is the remainder when open paren 3 x cubed minus 2 x squared plus 4 x minus 3 close paren is divided by open paren x squared plus 3 x plus 3 close paren ?

Using the divisor equation, x² ≡ −3x − 3. Multiplying by x and reducing again gives x³ ≡ 6x + 9. Substitute these into the polynomial: 3(6x + 9) − 2(−3x − 3) + 4x − 3 = 28x + 30. The remainder is 28x + 30, choice C.

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