Identify zeros from factorizations and use them to sketch polynomial graphs.
Extract zero behavior and end behavior from factored form
Problem
For \(p(x)~=~(x~+~2)(x~-~1)^2\), state the zeros, multiplicities, graph behavior at each zero, degree, leading-coefficient sign, and end behavior.
Big Picture
What this problem is really about
Factored form is a blueprint for both the local and global shape of the graph. We’ll read each zero and exponent, use multiplicity parity to decide what happens at that zero, then add the factor degrees and multiply their leading coefficients to determine the ends. Combining those local behaviors with the end pattern gives the full sketch.
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