What is a Polynomial?
A polynomial is a mathematical expression of variables and coefficients using only addition, subtraction, multiplication, and non-negative integer exponents. Examples include x^2 + 3x - 5 or 4x^4 - x + 7.
Polynomial Calculator
Add, subtract, multiply, derive, and integrate polynomials with a visual graph, roots finder, and step-by-step solutions. All calculations run in your browser.
Degree
Operation
Polynomial P(x)
x +
Result
Roots / Zeros
Graph of P(x)
Step-by-step solution
About Polynomials
Degree and Leading Coefficient
The degree is the highest power of x with a non-zero coefficient. The leading coefficient is the coefficient of that highest-power term. These determine end behavior and the maximum number of roots.
Derivatives and Integrals
The derivative of ax^n is n*a*x^(n-1). The integral of ax^n is (a/(n+1))*x^(n+1) + C. Derivatives find the rate of change; integrals find the area under the curve.
Roots and Zeros
Roots are the x-values where the polynomial equals zero. A polynomial of degree n has at most n roots (counting multiplicity). Linear and quadratic roots have exact formulas; higher degrees often require numerical methods.
Frequently Asked Questions
How do I enter a polynomial?
Choose a degree (Linear, Quadratic, Cubic, or Quartic) and fill in the coefficient fields. Each field maps to a term in the standard form. For polynomials of degree 5 or higher, use Custom mode and type in standard notation like 3x^5 - 2x^3 + x - 7.
What operations are supported?
Evaluate computes P(x) at a given x. Add, Subtract, and Multiply combine two polynomials. Derive finds the first derivative P'(x). Integrate finds the indefinite integral with a constant of integration C.
Can this calculator find roots?
Yes. For linear and quadratic polynomials exact roots are computed. For cubic and quartic polynomials numerical roots are found using Newton's method starting from multiple initial guesses. Complex roots are shown for quadratics with a negative discriminant.
Is the graph accurate?
The graph auto-scales to show roots, turning points, and end behavior. It recalculates in real time as you change coefficients. Root locations are marked as dots on the x-axis.
Does this calculator store my data?
No. All calculations run entirely in your browser. Nothing is sent to any server.
Privacy & Limitations
- All calculations run entirely in your browser -- nothing is sent to any server.
- Results are computed using standard formulas and should be verified for critical applications.
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Polynomial Calculator FAQ
How do I enter a polynomial?
Choose a degree (Linear through Quartic) or Custom mode. In preset degrees, fill in the coefficient fields which are laid out visually as an equation. In Custom mode, type the polynomial using standard notation like 3x^2 + 2x - 5.
What operations are supported?
Evaluate a polynomial at a point, add two polynomials, subtract, multiply, find the derivative, or find the integral. Each operation shows step-by-step work.
Can this calculator find roots?
Yes. For linear and quadratic polynomials, exact roots are computed analytically. For cubic and quartic polynomials, numerical approximations are found using Newton's method.
Is the polynomial graph accurate?
The graph auto-scales to show the important features of the polynomial including roots, turning points, and end behavior. It updates in real time as you change coefficients.