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Divisor: 2x - 4

In this problem above, the dividend lacks a variable to the second power, so we have to add a 0x^2 to make it:

4x^3 + 0x^2 - 6x - 11

Question:

Why do we add 0x^n? (n = missing powers)

In regular long division, we do no such thing. Why do we have to add these extra variables into the dividend in polynomial long division?

TVM!