When dividing a third-degree polynomial (let's denote it as \( P(x) \)) by a second-degree polynomial (denote it as \( D(x) \)), the result can be expressed in the form:
\[ P(x) = D(x) Q(x) + R(x) \]
where:
- \( Q(x) \) is the quotient, which will be a first-degree polynomial (or a linear polynomial) or could even be a constant (degree 0).
- \( R(x) \) is the remainder, which will be a polynomial of a degree less than that of the divisor \( D(x) \). Since \( D(x) \) is a second-degree polynomial, \( R(x) \) will be a polynomial of degree less than 2, which means \( R(x) \) can either be of degree 1, degree 0, or it can be the zero polynomial.
Thus, the statement that is always true when dividing a third-degree polynomial by a second-degree polynomial is:
The remainder will have a degree less than 2.
In other words, the remainder \( R(x) \) will be either a first-degree polynomial, a constant, or zero.