1. What is Polynomial Degree and Leading Coefficient?

The degree of a polynomial is the highest power of the variable in the polynomial, while the leading coefficient is the coefficient of the term with the highest degree. These are fundamental properties that determine the polynomial's behavior.

2. How Does the Calculator Work?

The calculator analyzes the polynomial expression:

Where:

• \( n \) — Degree (highest power)
• \( a_n \) — Leading coefficient
• \( x \) — Variable
• \( a_0 \) — Constant term

Explanation: The calculator identifies all terms, determines the highest power, and extracts the coefficient of that term.

3. Importance of Degree and Leading Coefficient

Details: The degree determines the polynomial's end behavior and maximum number of roots, while the leading coefficient affects the graph's steepness and direction.

4. Using the Calculator

Tips: Enter the polynomial in standard form using 'x' as the variable. Use ^ for exponents (e.g., 3x^2 - 2x + 1). The calculator will automatically identify the degree and leading coefficient.

5. Frequently Asked Questions (FAQ)

Q1: What is the degree of a constant polynomial?
A: The degree of a constant polynomial (e.g., P(x) = 5) is 0, and the leading coefficient is the constant itself.

Q2: How does the leading coefficient affect the graph?
A: A positive leading coefficient makes the graph rise to the right, while a negative one makes it fall to the right.

Q3: What if there are multiple terms with the same highest degree?
A: The leading coefficient is the sum of coefficients of all terms with the highest degree.

Q4: Can I use variables other than 'x'?
A: Currently, the calculator only recognizes 'x' as the variable. Other variables will be treated as constants.

Q5: What about polynomials with fractional coefficients?
A: The calculator handles fractional coefficients (e.g., 1/2, 0.75) and converts them to decimal form.