When you divide polynomials you may have to factor the polynomial to find a common factor between the numerator and the denominator. For example: Divide the following polynomial: (2x² + 4x) ÷ 2x. Both the numerator and denominator have a common factor of 2x. Thus, the expression can be written as 2x(x + 2) / 2x.

What happens when two polynomials divide?

We make the observation that whenever a polynomial is divided by a linear divisor, the remainder will always be a constant. The degree of the remainder r(x) will always be less than n. ...

When two polynomials are divided the quotient is always a polynomial?

There is no guarantee that a quotient of polynomials can be expressed as a polynomial, even though it sometimes can. As a simple example, note that both the numerator and denominator of 1x are polynomials, albeit trivial ones. Yet, this quotient is equivalent to x−1, which we know is not a polynomial.