Web Reference: Proof: We need to argue two things. First, we need to show that $q$ and $r$ exist. Then, we need to show that $q$ and $r$ are unique. To show that $q$ and $r$ exist, let us play around with a specific example first to get an idea of what might be involved, and then attempt to argue the general case. In arithmetic, long division is a standard division algorithm suitable for dividing multi-digit Hindu-Arabic numerals (positional notation) that is simple enough to perform by hand. It breaks down a division problem into a series of easier steps. Dec 18, 2018 · Given how tedious long division can be the method does reduce the work. You can structure your proof around this idea of subtracting and grouping so I'll leave you the pleasure of reconstructing the result for yourself.
YouTube Excerpt: Correction: The remainder of 2x^3-x+2is -13/9 x +20/9 when divided by 3x^2+x+1.
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