Finding the zeros and multiplicity by factoring polynomials with 3 and 4 terms

The video tutorial covers various techniques for factoring polynomials, including identifying common factors, understanding the role of constants, and using the zero product property. It explains how to factor trinomials and polynomials with four terms using the grouping technique. The tutorial also discusses the impact of constants on polynomial equations and graph transformations. The session concludes with a summary of the techniques and an introduction to writing polynomial equations from given zeros and multiplicities.

What is the first step in factoring a polynomial when a common factor is present?

• Multiply each term by the common factor

• Add the common factor to each term

• Factor out the common factor

• Ignore the common factor

How does a constant factor like 2 affect the graph of a polynomial?

• It shifts the graph horizontally

• It stretches or compresses the graph vertically

• It has no effect on the graph

• It changes the zeros of the polynomial

What is a perfect square trinomial?

• A trinomial that can be factored into two identical binomials

• A trinomial with no real roots

• A trinomial that cannot be factored

• A trinomial with three different terms

What does it mean for a zero to have a multiplicity of two?

• The zero is the only solution

• The zero is not a real number

• The zero appears twice on the graph

• The zero is a complex number

When factoring a trinomial with a leading coefficient other than 1, what is a common strategy?

• Guess and check

• Use the quadratic formula

• Factor by grouping

• Ignore the leading coefficient

What is the purpose of the grouping technique in polynomial factoring?

• To combine all terms into one

• To separate terms into pairs for easier factoring

• To eliminate terms

• To add new terms

In the grouping technique, what is the goal when factoring each group?

• To change the polynomial's degree

• To simplify the expression

• To find the greatest common factor

• To make each group identical

What is the next step after factoring out common terms in the grouping technique?

• Add the terms back together

• Multiply the terms

• Divide the terms

• Factor out the common binomial

What should you look for when factoring a polynomial with two terms?

• Difference of squares

• Perfect square trinomials

• Complex roots

• Grouping opportunities

What is the next topic after factoring polynomials?

• Solving quadratic equations

• Writing polynomial equations from given zeros

• Graphing polynomials

• Finding the derivative of polynomials