How to find the zeros and multiplicity by factoring 3 terms MP4

The video tutorial covers the process of factoring trinomials, starting with identifying common factors and using techniques like the AC method. It emphasizes understanding the structure of trinomials and solving them by producing binomials. The tutorial also discusses the concept of multiplicity and the zero product property, providing examples to illustrate these concepts.

What is the first step in factoring a trinomial with three terms?

• Identify and factor out the greatest common factor.

• Multiply the first and last coefficients.

• Add the coefficients of the middle term.

• Divide the trinomial by its leading coefficient.

When factoring trinomials, what is the result of the process?

• A difference of two squares.

• A sum of three monomials.

• A product of two binomials.

• A single polynomial.

What method is suggested for factoring trinomials when the leading coefficient is not one?

• Synthetic division.

• The quadratic formula.

• The AC method.

• Guess and check method.

What does the term 'multiplicity' refer to in the context of polynomial roots?

• The number of times a root is repeated.

• The sum of all roots.

• The degree of the polynomial.

• The number of distinct roots.

How does a repeated factor affect the graph of a polynomial?

• It increases the degree of the polynomial.

• It results in a horizontal shift.

• It changes the behavior at the x-intercept.

• It creates a vertical asymptote.