Leading coefficient is defined as?

Leading coefficient is defined as?

• A. The constant term
• B. The coefficient of the second highest degree term
• C. The coefficient of the term with the highest degree
• D. The coefficient of the lowest degree term

Answer: (C)

The leading coefficient is the coefficient of the term with the highest power of x. In a polynomial written as a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x + a_0, the leading coefficient is a_n. This term dominates the graph’s end behavior for very large or very small x, so its sign and size largely determine how the graph behaves as x grows in magnitude. The other terms influence the shape in the middle, but the highest-degree term sets the overall direction of the ends.

The leading coefficient is the coefficient of the term with the highest power of x. In a polynomial written as a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x + a_0, the leading coefficient is a_n. This term dominates the graph’s end behavior for very large or very small x, so its sign and size largely determine how the graph behaves as x grows in magnitude. The other terms influence the shape in the middle, but the highest-degree term sets the overall direction of the ends.