Rational Zeros Calculator

The Rational Root Theorem helps us find a list of all possible rational roots (zeros) of a polynomial with integer coefficients.

For a polynomial \(P(x) = a_nx^n + \dots + a_1x + a_0\), any rational root must be of the form \(\frac{p}{q}\), where:

• p is an integer factor of the constant term, \(a_0\).
• q is an integer factor of the leading coefficient, \(a_n\).

Steps:

1. List all factors of the constant term (\(p\)).
2. List all factors of the leading coefficient (\(q\)).
3. Create a list of all possible fractions \(\pm\frac{p}{q}\).
4. Test each of these possible roots by substituting them into the polynomial. If \(P(\frac{p}{q}) = 0\), then it is an actual root.