Determine the multiplicity and zeros and graph of a polynomial

The video tutorial covers the process of sketching polynomial graphs, focusing on finding zeros and determining their multiplicity. It explains the use of the leading coefficient test to predict the end behavior of the graph. The tutorial emphasizes understanding the polynomial's degree and how it affects the graph's shape, including crossing and touching points. The instructor encourages using graphing technology but highlights the value of manual graph sketching for deeper comprehension.

Describe the leading coefficient test and its significance in graphing.

What is the behavior of the graph as x approaches positive and negative infinity?

Sketch the graph of a polynomial function of degree five with given zeros and multiplicities.