Polynomial Calculator – Guide & Formulas
Analyze polynomial equations up to degree 4. Evaluates degrees, leading coefficients, synthetic division steps, and approximate roots.
Analyze polynomial equations step-by-step. Enter the coefficients for polynomial functions up to degree 4 to evaluate degrees, terms, and find both rational and real roots.
Key Takeaway
Use the free Polynomial Calculator to analyze polynomial equations up to degree 4. evaluates degrees, leading coefficients, synthetic division steps, and approximate roots. Get instant results with step-by-step explanations.
How to Use the Polynomial Calculator
- Enter the coefficients for your polynomial terms starting from the highest power (x^4 down to the constant c).
- Examine the resulting polynomial expression, its degree, and leading coefficient.
- Review the rational roots check and numerical root approximations.
The Formula
Variable Definitions
- n: The degree (highest power) of the polynomial
- a_n: The leading coefficient
- a_0: The constant term
Analyzing x³ - 6x² + 11x - 6
Analyze the cubic equation where coefficients are a3 = 1, a2 = -6, a1 = 11, and a0 = -6.
- Step 1: Input coefficients [1, -6, 11, -6].
- Step 2: The polynomial degree is 3, leading coefficient is 1.
- Step 3: Test rational candidates using Rational Root Theorem.
- Step 4: Find exact integer roots at x = 1, x = 2, and x = 3.
Frequently Asked Questions
What is the degree of a polynomial?
The degree is the highest exponent of any variable term in the polynomial when written in standard form.
What does the Rational Root Theorem state?
It states that any rational root of a polynomial with integer coefficients must be of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
How many roots can a polynomial have?
According to the Fundamental Theorem of Algebra, a polynomial of degree n will have exactly n roots (counting real, complex, and multiple roots).