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.

2. How Does The Calculator Work?

The calculator evaluates the polynomial at the given value:

Where:

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

Explanation: The calculator substitutes x = a into the polynomial and computes the result.

3. Importance Of Factor Theorem

Details: The Factor Theorem is fundamental in algebra for factoring polynomials, finding roots, and solving polynomial equations.

4. Using The Calculator

Tips: Enter the polynomial using standard notation (e.g., x^3 - 2x^2 + x - 2) and the value a to evaluate. Use proper mathematical syntax.

5. Frequently Asked Questions (FAQ)

Q1: What if f(a) = 0?
A: If f(a) = 0, then (x - a) is a factor of the polynomial f(x).

Q2: What notation should I use for exponents?
A: Use the caret symbol (^), for example: x^2 for x squared.

Q3: Can I use decimal values for a?
A: Yes, the calculator supports both integer and decimal values for a.

Q4: What if I get an error?
A: Check your polynomial syntax and ensure you're using valid mathematical operations.

Q5: Does this work for all types of polynomials?
A: Yes, the Factor Theorem applies to all polynomials, though complex roots may require additional methods.