LEADING COEFFICIENT

Leading Coefficient

Definition Of Leading Coefficient

In a polynomial, the coefficient of the term with the highest degree is called the leading coefficient.

Example of Leading Coefficient

The leading coefficient of the polynomial - 7x³ + 6x² + 2x - 5 is -7.

Video Examples: Leading Coefficients Another Problem Solved

Solved Example on Leading Coefficient

Ques: Choose the leading coefficient of the given polynomial function g(u) = 11u - 9u².

Choices:

A. - 11
B. - 9
C. 11
D. 9
Correct Answer: B

Solution:

Step 1: In a polynomial, the coefficient of the term with the highest degree is called the leading coefficient.
Step 2: The leading coefficient of the polynomial function g(u) = 11u - 9u² is -9.

Quick Summary

The leading coefficient is the number in front of the variable with the highest exponent.
The leading coefficient helps determine the end behavior of a polynomial function.

\[ a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x + a_0, \text{ leading coefficient is } a_n \]

🍎 Teacher Insights

Emphasize the importance of writing polynomials in standard form (descending order of exponents) to easily identify the leading coefficient.

🎓 Prerequisites

Polynomials
Coefficients
Degree of a Polynomial

Check Your Knowledge

Q1: What is the leading coefficient of the polynomial 3x^2 + 5x - 2?

A. -2 B. 5 C. 3 D. 2

Q2: What is the leading coefficient of the polynomial -7x^3 + 6x^2 + 2x - 5?

A. 6 B. 2 C. -5 D. -7

Frequently Asked Questions

Q: What happens if the polynomial is a constant?
A: If the polynomial is a constant (e.g., 5), the leading coefficient is that constant (5).

Q: Can the leading coefficient be zero?
A: No, if the leading coefficient is zero, the term with the highest degree would not exist, and it wouldn't be that degree of polynomial.