Question

How do you tell the possible rational roots of a polynomial function? How do you test one of the possible rational roots to see if it is indeed a zero?

Answer 1

Explanation:

To find the possible rational roots of a polynomial function, you can use the Rational Root Theorem. According to this theorem, if a rational number "p/q" is a root of a polynomial function, where p and q are integers, and q ≠ 0, then p must div ide the constant term of the polynomial and q must divide the leading coefficient of the polynomial.

To test if one of the possible rational roots is indeed a root (zero) of the polynomial, you can use the Synthetic Division method. In this method, you divide the polynomial by the linear factor (x - p/q) corresponding to the test root, and check if the remainder is zero. If the remainder is zero, then the test root is a zero (root) of the polynomial.