Algèbre
Polynomial Division Calculator | Divide Polynomials Online
Perform polynomial division online with our free calculator. Easily divide polynomials and find the quotient and remainder. Step-by-step solutions included.
Enter the polynomial to be divided.
Enter the polynomial to divide by.
Result
Quotient:
Remainder:
Error!
Understanding Polynomial Division
Polynomial division is a process in algebra for dividing a polynomial by another polynomial of the same or lower degree. It's similar to long division with numbers, but with variables and exponents. The result of dividing polynomials is a quotient and a remainder.
Formula
If we divide a polynomial P(x) (dividend) by another polynomial D(x) (divisor), we get a quotient Q(x) and a remainder R(x) such that:
$$ P(x) = D(x) \cdot Q(x) + R(x) $$
Use Cases
- Simplifying complex algebraic expressions.
- Finding roots of polynomials.
- Factoring polynomials.
- Solving polynomial equations.
- In calculus, for integration of rational functions.
Example
Divide x2 + 3x + 2 by x + 1:
- Dividend P(x) = x2 + 3x + 2
- Divisor D(x) = x + 1
- Quotient Q(x) = x + 2
- Remainder R(x) = 0
Thus, x2 + 3x + 2 = (x + 1)(x + 2) + 0.