Polynomial Division Calculator
Easily divide polynomials to find the quotient and remainder. Enter your dividend and divisor polynomials below.
Enter the polynomial to be divided.
Enter the polynomial to divide by.
Result
Quotient:
Remainder:
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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.