The statement in the image refers to the Rational Root Theorem. According to this theorem:

1. $p$ is a factor of the constant term $a_0$.
2. $q$ is a factor of the leading coefficient $a_n$.

Thus, the correct answers for the two blanks are:

• First blank: the constant term ($a_0$)
• Second blank: the leading coefficient ($a_n$)

This completes the statement correctly. Would you like further explanation or examples to understand the Rational Root Theorem?

Related Questions:

1. What is the purpose of the Rational Root Theorem?
2. How do you apply the theorem to a specific polynomial?
3. Can a polynomial with irrational roots satisfy the Rational Root Theorem?
4. What happens when $a_n = 1$? How does the theorem simplify?
5. How do synthetic division and the Rational Root Theorem relate?

Tip: Always reduce $\frac{p}{q}$ to its lowest terms before applying the theorem!