1. What is the Factor Theorem?

The Factor Theorem states that for a polynomial f(x), if f(a) = 0, then (x - a) is a factor of the polynomial. Conversely, if (x - a) is a factor, then f(a) = 0. This theorem is fundamental in polynomial algebra and root finding.

2. How Does the Calculator Work?

The calculator evaluates the polynomial at the given value using the formula:

Where:

• \( f(x) \) — Polynomial function
• \( a \) — Value to evaluate at

Explanation: The calculator parses the polynomial expression and computes its value at x = a using standard algebraic operations.

3. Importance of Factor Theorem

Details: The Factor Theorem is crucial for factoring polynomials, finding roots, and solving polynomial equations. It's widely used in algebra, calculus, and engineering applications.

4. Using the Calculator

Tips: Enter the polynomial in standard form (e.g., x^3 - 2x^2 + x - 2) and the value a. The calculator will compute f(a) using the Factor Theorem principle.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between Factor Theorem and Remainder Theorem?
A: The Factor Theorem is a special case of the Remainder Theorem where the remainder is zero, indicating that (x - a) is a factor.

Q2: How do I know if (x - a) is a factor?
A: If f(a) = 0, then (x - a) is a factor of the polynomial f(x).

Q3: What types of polynomials can this calculator handle?
A: The calculator can handle polynomials of any degree with real coefficients.

Q4: Are there limitations to this calculator?
A: The calculator works best with properly formatted polynomial expressions. Complex coefficients or special functions are not supported.

Q5: Can this calculator factor polynomials completely?
A: This calculator evaluates at a specific point. For complete factorization, you would need to find all roots systematically.