1. What is the Rational Zero Theorem?

The Rational Zero Theorem states that any rational zero of a polynomial function with integer coefficients must be 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 Zero Theorem formula:

Where:

• \( p \) — Constant term of the polynomial
• \( q \) — Leading coefficient of the polynomial
• Factors — All positive integers that divide the number evenly

Explanation: The theorem helps identify all possible rational roots that a polynomial equation might have, which is the first step in solving polynomial equations.

3. Importance of Rational Zero Theorem

Details: This theorem is crucial in algebra for solving polynomial equations, finding roots, and factoring polynomials. It significantly reduces the number of potential roots to test.

4. Using the Calculator

Tips: Enter the constant term (p) and leading coefficient (q) as integers. The calculator will display all factors and possible rational zeros. Non-zero integer inputs are required.

5. Frequently Asked Questions (FAQ)

Q1: What if the polynomial has no constant term?
A: If p = 0, then 0 is a root, and you should factor out x first before applying the theorem.

Q2: Are all listed zeros actual roots?
A: No, the theorem only provides possible rational roots. You must test each one to see if it's an actual root.

Q3: What about irrational or complex roots?
A: The Rational Zero Theorem only identifies possible rational roots. Irrational and complex roots require other methods to find.

Q4: How to handle fractions in coefficients?
A: Multiply the entire polynomial by the least common denominator to convert to integer coefficients first.

Q5: What if the leading coefficient is 1?
A: If q = 1, then the possible rational zeros are simply the factors of the constant term p.