Factoring polynomials to find the zeros and multiplicity

The video tutorial explains how to determine zeros and multiplicity by factoring polynomials. It covers linear factorization, the difference of squares, and perfect square trinomials. The instructor demonstrates these concepts through examples, emphasizing the importance of writing expressions as products of linear factors to identify zeros and their multiplicities. The tutorial also highlights common mistakes and provides strategies for factoring higher-degree polynomials.

What is the main objective when working with polynomial expressions in this lesson?

Explain the process of factoring a polynomial and why it is important.

What mistake do students often make when taking square roots to solve quadratic equations?

How can you identify the multiplicity of a zero from a factored polynomial?

Describe the difference between odd and even multiplicities in terms of graph behavior.

What is the significance of the zero product property in solving polynomial equations?

How do you factor a trinomial into the product of two binomials?

What is a perfect square trinomial and how can it be factored?

Explain the substitution method for factoring polynomials raised to higher powers.

What are the steps to identify all real zeros of a polynomial function?