Understanding Polynomial Functions: Degree, Coefficients & Real Zeros

TLDR; The video explains how to find key information about a given polynomial function, including ordering terms, determining the degree, leading coefficient, maximum number of real zeros, and maximum number of turns.

📝 Descending Order of Polynomial Function

The polynomial function should be written in descending order, from the highest degree to the lowest.

For example, the polynomial function -3X^6 + 4X^3 - 2X^2 + 7X - 3 is written in descending order.

Each term is arranged based on its degree, with the term having the highest degree being listed first.

🔢 Degree of the Polynomial Function

The degree of the polynomial function is determined by the term with the highest degree.

In the given example, the degree of the polynomial function is 6, which is the degree of the term with the highest degree.

The leading coefficient is the coefficient of the term with the highest degree, which is -3 in the provided polynomial function.

📈 Maximum Number of Real Zeros and Turns

The maximum number of real zeros is equal to the maximum number of x-intercepts or horizontal intercepts, which is also equal to the degree of the polynomial function.

In this case, the maximum number of real zeros for the given polynomial function is 6.

Additionally, the maximum number of turns in a polynomial function is equal to the degree minus 1, which in this case is 5.