1. What is Polynomial Long Division?

Polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree. It's analogous to long division of numbers and provides a way to simplify polynomial expressions.

2. How Does the Calculator Work?

The calculator performs the standard polynomial division algorithm:

Where:

• Dividend — The polynomial being divided
• Divisor — The polynomial dividing the dividend
• Quotient — The result of the division
• Remainder — What's left after division (degree less than divisor)

Explanation: The algorithm repeatedly divides the highest degree terms, multiplies, subtracts, and brings down terms until the remainder's degree is less than the divisor's.

3. Importance of Polynomial Division

Details: Polynomial division is essential for factoring polynomials, finding roots, simplifying rational expressions, and in calculus for polynomial decomposition.

4. Using the Calculator

Tips: Enter polynomials in standard form (e.g., "x^3 + 2x^2 - 4x + 8"). The divisor must have equal or lower degree than the dividend.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between polynomial division and synthetic division?
A: Synthetic division is a shortcut that only works when dividing by linear divisors (x - c), while polynomial division works for any divisor.

Q2: Can the degree of the remainder be equal to the divisor?
A: No, the remainder must have a degree strictly less than the divisor's degree.

Q3: What happens if the divisor is a constant?
A: You're essentially dividing each term of the dividend by the constant (like factoring out a constant).

Q4: Can this handle polynomials with missing terms?
A: Yes, but it's helpful to include zero coefficients for missing terms (e.g., x^3 + 0x^2 + 2x + 1).

Q5: What's the connection to polynomial factorization?
A: If division results in zero remainder, the divisor is a factor of the dividend.