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Lecture

# CALC17.pdf

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School
University of California - Davis
Department
Mathematics
Course
MAT 17A
Professor
T R A V I S S C R I M S H A W
Semester
Winter

Description
Introductions (Polynomial) Long Division Travis Scrimshaw January 6, 2014 Division is the inverse operation to multiplication, so formally we want to find some x such that βx = α for some given values α (the dividend) and β ̸ = 0 (the divisor) in some R, which can be either Z, Z[x], Q[x], R[x], or C[x]. (For the curious reader, R could also be Q, R, or C, but these are too “big” because they all have a well defined β −1.) The question becomes how do we do that, and the answer is (polynomial) long division. Long division is an algorithm to find some q (the quotient) such that α = qβ + r where r (the remainder) satisfies 0 ≤ d(r)
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