Identify zeros from factorizations and use them to sketch polynomial graphs.
Determine the end behavior of a polynomial written in factored form
Problem
Determine the degree, leading-coefficient sign, and end behavior of \(-2(x~-~1)^3(x~+~4)\).
Big Picture
What this problem is really about
We do not need to expand the whole polynomial to find its end behavior. We’ll multiply only the leading parts of the factors: their degrees add to give the total degree, and their leading coefficients multiply to give the leading sign. The degree’s parity sets whether the ends match, while the sign sets their orientation.
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