Addition
\((2x^2 + 3x) + (x^2 - x + 5) = 3x^2 + 2x + 5\)
Polynom-Rechner
Arbeiten Sie mit Polynomausdrücken: addieren, subtrahieren, multiplizieren, dividieren und faktorisieren
Ergebnisse
Geben Sie Werte ein und klicken Sie auf Berechnen, um das Ergebnis zu sehen.
Theory & Formula
A polynomial is an expression consisting of variables and coefficients, involving operations of addition, subtraction, multiplication, and non-negative integer exponents.
Polynomial operations follow these rules:
- Addition/Subtraction: Combine like terms (same power of x)
- Multiplication: Multiply each term by every other term, add exponents when multiplying same bases
- Degree: The highest power of the variable in the polynomial
\(P(x) = a_nx^n + a_{n-1}x^{n-1} + \cdots + a_1x + a_0\)
Worked Examples
Subtraction
\((3x^2 + 2) - (x^2 + 4x - 1) = 2x^2 - 4x + 3\)
Multiplication
\((x + 2)(x - 3) = x^2 - x - 6\)
Derivative
\(\frac{d}{dx}(3x^2 + 2x) = 6x + 2\)
Integral
\(\int (2x + 3)\,dx = x^2 + 3x + C\)