Question

Use the rational zeros theorem to list the potential rational zeros of the polynomial function. Do not attempt to find the zeros.

a) Rational zeros theorem
b) Potential rational zeros
c) Polynomial function
d) Finding zeros

Answer 1

The rational zeros theorem aids in identifying all possible rational zeros of a polynomial function, which are ratios of factors of the constant term to factors of the leading coefficient.

Step-by-step explanation:

Rational Zeros Theorem

The rational zeros theorem is a mathematical principle used to identify all potential rational zeros of a polynomial function. To utilize this theorem, one would look at the polynomial's constant term and the leading coefficient. The potential rational zeros are all the possible ratios (fractions) formed by dividing the factors of the constant term by the factors of the leading coefficient.

Potential Rational Zeros

If we have a polynomial function f(x) = anxn + ... + a0, where an is the leading coefficient and a0 is the constant term, the potential rational zeros can be determined. They are given by the list of fractions ±p/q, where p is a factor of the constant term a0, and q is a factor of the leading coefficient an. This list includes all integer and proper fractional factors that could potentially be zeros of the polynomial.