Polynomial Functions
Comprehensive tools for all polynomial operations
Basic Operations
Multiplication Operations
Division Operations
About Polynomial Operations
Polynomials are mathematical expressions of the form \(P(x) = a_n x^n + a_{n-1} x^{n-1} + \ldots + a_1 x + a_0\), where the \(a_i\) are real coefficients.
Basic Operations:
- Addition/Subtraction: Coefficients of like powers are added/subtracted
- Multiplication: Each term of the first polynomial is multiplied by each term of the second
- Division: Polynomial division with quotient and remainder
Special Operations:
- Pointwise: Element-wise operation of coefficients
- Scalar: Multiplication/division by a constant
- Advanced: Zeros, derivatives, integration
Input Format
Example: For the polynomial \(3x^2 + 4x + 5\) enter: 3 4 5
Coefficients are entered in descending order of powers, separated by spaces or semicolons.
Application Areas
Natural Sciences
Modeling physical phenomena, growth processes, oscillations
Economics
Cost analysis, profit functions, market models
Engineering
Signal processing, control systems, approximations
Mathematics
Algebraic structures, analysis, numerics