Polynomials are mathematical expressions that contain constants, variables, powers with non-negative integers, and operations. A factor of a polynomial is an expression that, when multiplied by another expression, results in the original polynomial. For example, if the polynomial F(X) is given and (X + 3) is a factor of F(X), then F(X) can be written as (X + 3) multiplied by another expression. This means that the result of the multiplication is equal to the original F(X).

Therefore, if (X + 3) is a factor of F(X), then the following must be true:

- F(X) can be written as (X + 3) multiplied by another expression.
- The product of (X + 3) and the other expression is equal to F(X).

Another important conclusion is that the other expression is also a factor of F(X). Since F(X) can be written as a product of two expressions, q and (X + 3), then q must also be a factor of F(X).

For example, consider the expression F(X) = (X + 3)(X + 4). In this case, (X + 3) is a factor of F(X). We can therefore conclude that F(X) can be written as (X + 3) multiplied by an expression, and that the other expression is (X + 4). Since (X + 4) is equal to F(X) divided by (X + 3), then (X + 4) is also a factor of F(X).

In conclusion, if (X + 3) is a factor of a polynomial F(X), then the polynomial F(X) can be written as (X + 3) multiplied by another expression. Furthermore, the other expression is also a factor of F(X).