Polynomial Long Division Calculator

Polynomial division is a core skill for advanced algebra. Use this tool as follows:

Step 1: Enter the "Dividend" polynomial (e.g., x^3 - 2x^2 + 0x - 4). Note: Use 0 for missing terms to maintain proper alignment.

Step 2: Enter the "Divisor" polynomial (e.g., x - 2).

Step 3: Click "Divide."

Step 4: Review the results. The calculator will provide: - The Quotient (the result of the division). - The Remainder (the leftover part). - A formatted "Synthetic Division" or "Long Division" table showing each subtraction step.

Step 5: Use the Remainder Theorem check to verify that P(divisor root) = Remainder.

The process is similar to long division with numbers:

1. Setup: Write the dividend and divisor in descending order of exponents. 2. Divide: Divide the first term of the dividend by the first term of the divisor. This is the first term of the quotient. 3. Multiply: Multiply that result by the entire divisor. 4. Subtract: Subtract that product from the dividend to find the new "current" polynomial. 5. Repeat: Repeat the process until the degree of the remaining polynomial is less than the divisor's degree.

The result is written as: Quotient + (Remainder / Divisor)

The Polynomial Long Division Calculator is an essential aid for factoring polynomials and finding roots. In calculus, this technique is used to simplify rational functions before integration. It is also a fundamental part of the 'Factor Theorem'—if the remainder of a division is zero, you have successfully found a factor of the polynomial. By automating the sign-flipping and term-alignment that cause most manual errors, this tool helps students master algebraic manipulation and prepare for more advanced mathematical analysis.