Know the Fundamental Theorem of Algebra and connect it to polynomial roots.
Count the complex roots of a factored polynomial, including multiplicity
Problem
For \((x~-~2)^{3}(x~+~1)\), list each root with its multiplicity and give the total root count including multiplicity.
Big Picture
What this problem is really about
Factored form records both root values and how often they occur. Set each distinct linear factor equal to zero, then attach the factor's exponent as that root's multiplicity. Keep the distinct-root count separate from the total count, and verify the latter by adding the multiplicities and comparing the sum with the polynomial's degree.
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