Know the Fundamental Theorem of Algebra and connect it to polynomial roots.
Build the monic polynomial from roots and multiplicities
Problem
Build and expand the monic real-coefficient polynomial with roots \(2\) and \(-3\).
Big Picture
What this problem is really about
Convert every root r into a factor x minus r, paying special attention to the double negative created by a negative root. Repeat factors when multiplicities are given and pair nonreal roots with their conjugates when real coefficients are required. The monic condition fixes the leading multiplier at one, leaving only the factor product to expand and verify.
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