1. What is the Rational Zero Theorem?

The Rational Zero Theorem provides a method to find all possible rational zeros of a polynomial function with integer coefficients. It states that if a polynomial has integer coefficients, then every rational zero will have 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 Zero Theorem formula:

Where:

• \( p \) — Factors of the constant term (last term)
• \( q \) — Factors of the leading coefficient (first term coefficient)
• All fractions are reduced to simplest form
• Both positive and negative possibilities are considered

Explanation: The theorem helps narrow down the search for rational roots among all possible fractions.

3. Importance of Rational Zero Theorem

Details: This theorem is crucial for solving polynomial equations, factoring polynomials, and finding x-intercepts of polynomial functions in algebra and calculus.

4. Using the Calculator

Tips: Enter all factors of the constant term (comma separated), then enter all factors of the leading coefficient (comma separated). The calculator will generate all possible rational zeros in simplest form.

5. Frequently Asked Questions (FAQ)

Q1: Does this guarantee actual zeros?
A: No, it only provides possible candidates. You must test each candidate in the polynomial to confirm if it's an actual zero.

Q2: What if there are no rational zeros?
A: The polynomial may have irrational or complex zeros instead. The theorem only applies to rational zeros.

Q3: How do I find factors of numbers?
A: Factors are numbers that divide evenly into the given number. For example, factors of 6 are 1, 2, 3, 6.

Q4: What about repeated factors?
A: The calculator automatically removes duplicates, so you only get unique possible zeros.

Q5: Can this handle large numbers?
A: Yes, but very large numbers may require more computation time. The calculator efficiently processes the factors.