Interpret terms, factors, and coefficients in polynomial and rational expressions.
Read leading coefficient, parity, and both polynomial ends
Problem
For \(p(x)~=~-3x^4~+~2x~-~1\), state the leading term, its sign and degree parity, and the behavior of \(\text{both}~\text{ends}\).
Big Picture
What this problem is really about
For end behavior, ignore lower-degree terms and begin with the term having the greatest exponent. The exponent's parity tells whether the two ends move together or in opposite directions, while the leading coefficient's sign orients the right end. Combine those two facts to describe both limits rather than reasoning from the constant or linear term.
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