Polynomial Division Calculator

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:

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.