What is a leading term?

A leading term in a polynomial is the term with the highest degree. It is the term that determines the overall behavior of the polynomial as the input values become very large or very small.

For example, in the polynomial 3x^4 + 2x^2 - 5x + 1, the leading term is 3x^4 because it has the highest degree (4) among all the terms.

The leading term is important in determining the end behavior of a polynomial function. If the leading term is positive and has an even degree, the function will rise to the right and left as x approaches positive or negative infinity. If the leading term is negative and has an even degree, the function will fall to the right and left as x approaches positive or negative infinity. If the leading term has an odd degree, the function will rise to the right and fall to the left as x approaches positive infinity, and fall to the right and rise to the left as x approaches negative infinity.

Overall, the leading term plays a significant role in analyzing and understanding the behavior of a polynomial function.