Identify zeros from factorizations and use them to sketch polynomial graphs.
Enter each polynomial zero with its multiplicity
Problem
State each zero and its multiplicity for \(p(x)~=~(x~-~2)^3(x~+~1)^2\).
Big Picture
What this problem is really about
Each repeated factor carries two pieces of information: the value that makes its base zero and the exponent that counts how many times it repeats. We’ll solve the base of each factor, then keep that exponent attached to the zero as its multiplicity. Rewriting x plus 1 as x minus negative 1 keeps the second sign clear.
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