1. What is the Rational Root Theorem?

The Rational Root Theorem states that any possible rational zero of a polynomial with integer coefficients is of the form ±p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

2. How Does the Calculator Work?

The calculator uses the Rational Root Theorem:

Where:

• Constant term — The term without x in the polynomial
• Leading coefficient — The coefficient of the highest power term

Explanation: The calculator finds all factors of the constant term and leading coefficient, then computes all possible ±p/q combinations.

3. Importance of Potential Zeros

Details: Finding potential rational zeros helps in factoring polynomials and solving polynomial equations, which is fundamental in algebra and calculus.

4. Using the Calculator

Tips: Enter the constant term and leading coefficient of your polynomial. The calculator will list all possible rational zeros that you can test in your polynomial.

5. Frequently Asked Questions (FAQ)

Q1: Does this guarantee actual zeros of the polynomial?
A: No, it only provides potential candidates. You need to test each one to see if it's actually a zero.

Q2: What if my polynomial has non-integer coefficients?
A: The theorem only applies to polynomials with integer coefficients. You may need to multiply through by denominators first.

Q3: Why do we consider both positive and negative factors?
A: The ± in the theorem means we must consider both positive and negative possibilities for each fraction.

Q4: What if there are no rational zeros?
A: The polynomial might only have irrational or complex zeros in that case.

Q5: How do I test if a potential zero is actually a zero?
A: Substitute the value into the polynomial - if it equals zero, then it's an actual zero.