The Factor Theorem Calculator helps you verify if a polynomial is divisible by a linear factor. By entering the polynomial and the potential factor, the calculator will determine whether the factor is a root of the polynomial.
Understanding the Factor Theorem
The Factor Theorem is a special case of the polynomial remainder theorem. It states that a polynomial f(x) has a factor (x – c) if and only if f(c) = 0. This theorem is particularly useful in finding the roots of polynomials and simplifying polynomial division.
f(c) = 0 implies (x - c) is a factor of f(x)
Variables:
- f(x) is the polynomial function
- c is the root of the polynomial
To apply the Factor Theorem, substitute the value of the root into the polynomial. If the result is zero, then the given factor is indeed a root of the polynomial. Otherwise, it is not a factor.
Applications of the Factor Theorem
The Factor Theorem is widely used in algebra for polynomial factorization and in solving polynomial equations. It helps in:
- Finding the roots of polynomial equations.
- Determining the irreducibility of polynomials.
- Simplifying complex polynomial expressions.
- Identifying factors for polynomial division.
- Solving real-world problems involving polynomial functions.
Example Problem:
Use the following example to test the Factor Theorem.
Polynomial = x^3 – 3x^2 + 2x
Factor = x – 1
FAQ
1. What is a polynomial?
A polynomial is an algebraic expression consisting of variables and coefficients, involving operations of addition, subtraction, multiplication, and non-negative integer exponents.
2. How