Extract a polynomial leading term and both end limits
Problem
For \(P(x)~=~(x~-~2)^2(3x~+~1)\), determine the leading term, degree, leading coefficient, and \(\text{both}~\text{end}~\text{limits}\).
Big Picture
What this problem is really about
End behavior comes from the highest-degree contribution, so a factored polynomial need not be fully expanded. Take the leading part of each factor and multiply those parts to get the overall leading term. Its exponent tells whether the ends match or oppose, and its coefficient’s sign tells which way the right end points.
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