MTH 282 Lecture Notes - Lecture 3: Exclusive Economic Zone
7 May 2020
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A polynomialof degree h b of the form pncz. Division algorithm letfcz be a polynomialof degree n and letg. cz be a polynomial of degree mzo then 7 polynomialsgeez rczss. t. fczs qczsgczstrczswhee. kz has degree m fczi gcz eez 1722 got. If zz is a rootofqcz then can write fczkgnscz z zx z zz then get fczsqczcz zi constant sincedegcg3 1. O fez1 0621 o costar since degcz 21 1 constant o. If zz is a zeroof eenl z then can continue fczkgenzcz z zike 227 continuelikethis providedyou can find words write fcz cczz c222 c2zn. Every nonconstant polynomial withcomplexcoefficients has at least one. Zero m cl cguarantee roots exist but doesn"tsayhow to findthem. Gi anypolynomial with complex coefficients may be factoredas a product of linearterms pnczkancz z czzz. Pnez completely determined by roots 2i zn and coefficient an of zn. Zo is a zeroof multiplicity k iff pnas cz 2ofqcz whereqcz is a polynomial with qczo 0.
