1. What is the Remainder Theorem?

The Remainder Theorem states that the remainder of the division of a polynomial f(x) by a linear divisor (x - c) is equal to f(c). This provides a quick way to evaluate polynomials at specific points.

2. How Does the Calculator Work?

The calculator uses the Remainder Theorem formula:

Explanation: Instead of performing polynomial division, we simply evaluate the polynomial at x = c to find the remainder.

3. Importance of the Remainder Theorem

Details: The Remainder Theorem is fundamental in algebra and calculus. It's used for polynomial evaluation, factorization, and in understanding polynomial behavior. It's also the basis for the Factor Theorem.

4. Using the Calculator

Tips:

• Enter the polynomial using standard notation (e.g., x^3 - 2x^2 + 3x - 4)
• Use ^ for exponents (x^2 for x squared)
• Enter the value of c for which you want to evaluate the polynomial

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between Remainder and Factor Theorems?
A: The Factor Theorem is a special case where if f(c) = 0, then (x - c) is a factor of f(x).

Q2: Does this work for all polynomials?
A: Yes, the Remainder Theorem applies to all polynomial functions.

Q3: Can I use this for complex numbers?
A: The theorem holds for complex numbers, but this calculator currently handles real numbers only.

Q4: What if I get an error message?
A: Check your polynomial syntax. Make sure to use proper notation (e.g., 3x^2 not 3x2).

Q5: How is this related to synthetic division?
A: Synthetic division is an algorithm that implements the Remainder Theorem efficiently.