State division algorithm for polynomials.

Explanation

### Step-by-Step Solution

1. **Understanding the Division Algorithm for Polynomials**: The Division Algorithm for polynomials is a method that allows us to divide one polynomial by another and express the result in a specific form.

2. **Statement of the Division Algorithm**:
- Let \( f(x) \) and \( g(x) \) be two polynomials where \( g(x) \neq 0 \).
- According to the Division Algorithm, we can express the polynomial \( f(x) \) as:
\[ f(x) = q(x) \cdot g(x) + r(x) \]
- Here, \( q(x) \) is the quotient, \( g(x) \) is the divisor, and \( r(x) \) is the remainder.

3. **Conditions on the Remainder**:
- The remainder \( r(x) \) must satisfy the condition that its degree is less than the degree of \( g(x) \).
- Mathematically, this can be stated as:
\[ \text{degree of } r(x) < \text{degree of } g(x) \]
- In some cases, the remainder can also be zero, which means that \( f(x) \) is exactly divisible by \( g(x) \).

4. **Understanding Degree**:
- The degree of a polynomial is the highest power of the variable in the polynomial.
- For example, in the polynomial \( x^2 + 3x + 2 \), the degree is 2 because the highest power of \( x \) is 2.

### Final Statement
Thus, the Division Algorithm for polynomials can be summarized as follows:
If \( f(x) \) and \( g(x) \) are polynomials with \( g(x) \neq 0 \), then there exist unique polynomials \( q(x) \) (the quotient) and \( r(x) \) (the remainder) such that:
\[ f(x) = q(x) \cdot g(x) + r(x) \]
where the degree of \( r(x) \) is less than the degree of \( g(x) \).