What is the quotient of open paren x cubed plus 3 x squared minus 4 x minus 12 close paren divided by open paren x squared plus 5 x plus 6 close paren ?

Factor the numerator by grouping: x³ + 3x² − 4x − 12 = (x + 3)(x² − 4) = (x + 3)(x − 2)(x + 2). The denominator factors as x² + 5x + 6 = (x + 2)(x + 3). Cancel the common factors to get x − 2, so the quotient is x minus 2.

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