Using synthetic division:

x^3 + 4x^2 - 3x - 12 / x^2 - 3

Write it out like a long division problem. x^-3 goes into x^3 + 4x^2 -3x -12x times. This is the first term of the answer. Multiply x by x^2 -3 and write the product under the dividend. That would be x^3 -3x. Subtract x^3 - 3x from the dividend and you have 4x^2 -12 left over. How many times does x-3 go into that? Add that to the x in the quotient.

The answer is x+4

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