Rewrite functions in equivalent forms to reveal and explain useful properties.
Determine polynomial end behavior directly from the leading term
Problem
For \(P(x)~=~(x~-~2)(x~+~5)(3x~-~1)\), identify the leading part of each factor, find the leading term, state the degree and leading-coefficient sign, and give \(\text{both}~\text{exact}~\text{end}~\text{limits}\).
Big Picture
What this problem is really about
End behavior does not require expanding the entire product. Take only the leading part of each factor and multiply those pieces to obtain the polynomial’s leading term. Its degree parity determines whether the tails agree or oppose, and its coefficient sign fixes the right tail; translate the resulting directions into two precise limit statements.
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