Identify zeros from factorizations and use them to sketch polynomial graphs.
Use the degree of a polynomial to find the greatest possible number of turning points
Problem
Find the maximum possible number of turning points for a degree \(3\) polynomial.
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What this problem is really about
The degree controls how much a polynomial can turn, but the bound is a maximum rather than a guarantee. A degree-n polynomial can have at most n minus one turning points, so identify the degree and apply that cap. Do not confuse turning points with zeros, since neither count determines the other exactly.
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