How to write a polynomial in standard form when divided by a number

The video tutorial explains the concept of polynomials, focusing on the distributive property and division. It guides students through identifying polynomials, simplifying expressions, and understanding the leading coefficient and degree. The tutorial emphasizes the importance of correctly applying division and multiplication in polynomial expressions and concludes with a clear example of writing a polynomial in its final form.

How does the presence of a variable in the denominator affect whether an expression is a polynomial?

Describe the process of simplifying the expression mentioned in the text.