<s>[INST] How does polynomial long division work? 
I get normal long division but this doesn't make sense. How can doing it by only dividing by the leading term work? The problem is $$\dfrac{3x^3 - 2x^2 + 4x - 3 } {x^2 + 3x + 3},$$ not $$\dfrac{3x^3 - 2x^2 + 4x - 3} {x^2}.$$
 [/INST] Some trick on how to do this quickly: $3x^3 - 2x^2 + 4x - 3 = 3x(x^2+3x+3) - 11x^2 - 5x - 3 = 3x(x^2+3x+3) - 11(x^2+3x+3) + 28x + 30 = (3x-11)(x^2+3x+3) + 28x+30$.
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