Polynomials and Rational Functions
The reader will be familiar with expressions such as 2x2 + 3x + 4 which are combinations of powers of. These are known as polynomials. In the first two sections, we prove the basis results about polynomials. In many respects, these are reminiscent of results about Z. Trivially, polynomials may be added multiplied to produce new polynomials (i.e. the set of polynomials is closed under addition multiplication). More significantly, we have ideas of division with remainder factorisation. The former generalises the process of synthetic division with which the reader may be familiar. Just as we define rational numbers as quotients of integers, we define rational functions as quotients of polynomials. We ...
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