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, similar to arithmetic long division.

2. How Does Polynomial Division Work?

The division follows this basic formula:

Where:

• Dividend — The polynomial being divided
• Divisor — The polynomial dividing the dividend
• Quotient — The result of the division
• Remainder — What's left after division (if any)

Explanation: The algorithm repeatedly divides the highest degree term of the current remainder by the highest degree term of the divisor.

3. Importance of Polynomial Division

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

4. Using the Calculator

Tips: Enter polynomials in standard form (e.g., "x^2 + 3x + 2"). The calculator will perform the division and show the quotient.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between polynomial and arithmetic division?
A: Polynomial division works with variables and exponents, following similar steps but dealing with terms rather than digits.

Q2: When does polynomial division have a remainder?
A: When the dividend isn't perfectly divisible by the divisor, similar to integer division.

Q3: Can you divide by a higher-degree polynomial?
A: No, the divisor must have equal or lower degree than the dividend for standard polynomial division.

Q4: What are common uses of polynomial division?
A: Factoring polynomials, partial fraction decomposition, and solving polynomial equations.

Q5: How is synthetic division different?
A: Synthetic division is a shortcut method that only works when dividing by linear divisors of form (x - c).