Determine the Zeros for a Polynomial by Factoring

The video tutorial explains how to analyze a polynomial equation by determining its end behavior, finding its zeros, and understanding the multiplicity of these zeros. The process involves setting the function equal to zero, factoring the equation using the greatest common factor (GCF), and applying the zero product property. The tutorial concludes by solving for the zeros and discussing their multiplicity, which affects how the graph crosses the x-axis.

What is the end behavior of a polynomial with an odd degree and a positive leading coefficient?

• Rises left and falls right

• Falls left and rises right

• Rises left and rises right

• Falls left and falls right

What is the first step in finding the zeros of a polynomial?

• Factor out the greatest common factor

• Add all coefficients

• Multiply all terms

• Set the polynomial equal to 1

Which of the following pairs of numbers multiply to -6 and add to -1?

• 1 and -6

• 2 and -3

• -3 and 2

• -2 and 3

How many zeros does the polynomial have after factoring?

• Four

• Three

• Two

• One

What is the multiplicity of each zero in the given polynomial?

• Multiplicity of 1

• Multiplicity of 3

• Multiplicity of 2

• Multiplicity of 0