MAC1105 Lecture Notes - Lecture 18: Intermediate Value Theorem, Division Algorithm
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25 Feb 2017
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5. 2 real zeros of a polynomial function notes: sterling. Provide a generalization to each of the key terms listed in this section. = q (x) + r (x) g (x) (g (x))(cid:18) f (x) g (x)(cid:19) = (g (x))(cid:18)q (x) + r (x) g (x)(cid:19) f (x) = q (x) g (x) + r (x) If f (x) is being divided by x c, which would look like f (x) x c , then f (c) would be the remainder. The term x c would be a factor of f (x) i [if any only i ] f (c) = 0: ifthen scenario. If f (c) = 0, then x c would de nitely be a factor of f (x). If x c is a de nite factor of f (x), then f (c) = 0. A polynomial function with a degree of n has at more n real zeros, but i [if and only if] n 1.