Graph polynomial functions using zeros, factorizations, and end behavior.
Build the least-degree polynomial through a point
Problem
Write the least-degree polynomial with simple real zeros \(-1\) and \(3\) that passes through \((0,~6)\).
Big Picture
What this problem is really about
Start with one linear factor for each simple zero and an unknown scale multiplier out front. That factor skeleton has the least possible degree; substituting the given point determines the remaining multiplier without introducing any new zeros. Verify the finished model against both zero conditions and the point, then confirm that no unnecessary factors were added.
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