91Ó°ÊÓ

The leading term of a polynomial is the term with the highest degree (i.e., the highest power of the variable). For example, in the polynomial f(x) = 3x^4 - 5x^2 + 7, the leading term is 3x^4.

The degree of a polynomial is the highest power of the variable in the polynomial. In our example from Step 1, the degree of the polynomial is 4, which comes from the leading term 3x^4.

If the degree of the polynomial is even, the end behavior of the polynomial will be the same (both either rise or fall) at both ends. If the degree of the polynomial is odd, the end behavior of the polynomial will be opposite (one end will rise, and the other end will fall) at both ends. Furthermore, if the leading coefficient is positive, the behavior at the right end will be rising, and if the leading coefficient is negative, the behavior at the right end will be falling. Applying these rules to our example, the degree of the polynomial is even (4), and the leading coefficient is positive (3): - As the input variable approaches positive infinity (x -> +∞), both ends will have the same behavior, so f(x) will approach positive infinity (f(x) -> +∞). - As the input variable approaches negative infinity (x -> -∞), both ends will have the same behavior, so f(x) will also approach positive infinity (f(x) -> +∞). Summarizing the end behavior: As x -> ±∞, f(x) -> +∞.