The video tutorial explains the multiplication of polynomials using the FOIL method, emphasizing the importance of focusing on the leading terms to determine the highest degree and leading coefficient. It further explores how these factors influence the end behavior of polynomial graphs, providing examples of odd and negative leading coefficients.

Describe the behavior of the function as X approaches negative infinity based on the teacher's explanation.

What is the significance of the left-hand and right-hand behavior of the function as discussed in the lesson?