Section 4.3: Anaylsis

Polynomials in a field behave very similar to the arithmetic already seen. In this section Hungerford brings that comparison one step further. Prime numbers are integers which have only two positive factors, the number and one. Polynomials, however, have an equivalent, that is irreducible polynomials. When doing long division we get to a point where the polynomial doesn’t reduce anymore and/or there is some remainder polynomial. So it makes sense that there would be a version of polynomials that cannot be reduced to any other multiplicative combination of polynomials.

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