rational zero theorem
[rational zero theorem|rational zero theorem] states that if a polynomial with integer coefficients has a rational zero in the form p/q, then p is a factor of the constant term and q is a factor of the leading coefficient.
Definition
rational zero theorem states that if a polynomial with integer coefficients has a rational zero in the form p/q, then p is a factor of the constant term and q is a factor of the leading coefficient.
Mechanism
rational zero theorem identifies potential rational zeros by dividing the constant term's factors by the leading coefficient's factors. This process involves listing all possible fractions formed from these divisions to narrow down candidates for testing.
Effects
rational zero theorem identifies potential rational zeros of a polynomial by examining the ratio of factors of the constant term to factors of the leading coefficient. This process narrows down the list of possible rational zeros based on the polynomial's structure.