Question

the numerators of any rational roots of a polynomial will be factors of the ___.
constant term
sum of the coefficients
degree of the polynomial
leading coefficient

1. choose the best answer.

the denominators of any rational roots of a polynomial will be factors of the ___.
leading coefficient
degree of the polynomial
constant term
sum of the coefficients

Explanation:

First Question:

The Rational Root Theorem states that for a polynomial \( a_nx^n + a_{n - 1}x^{n - 1}+\dots+a_1x + a_0\) (where \(a_n
eq0\)), any rational root \( \frac{p}{q}\) has \(p\) as a factor of the constant term \(a_0\) and \(q\) as a factor of the leading coefficient \(a_n\). So for the numerators of rational roots, they are factors of the constant term.

From the Rational Root Theorem, for a rational root \( \frac{p}{q}\) of a polynomial \( a_nx^n + a_{n - 1}x^{n - 1}+\dots+a_1x + a_0\) (\(a_n
eq0\)), the denominator \(q\) of the rational root is a factor of the leading coefficient \(a_n\).

Answer:

A. constant term

Second Question: