Determine the Zeros for a Polynomial by Factoring

The video tutorial explains how to analyze a polynomial function, focusing on determining its end behavior, finding zeros, and understanding multiplicity. The instructor begins by identifying the degree and leading coefficient to predict the graph's behavior. The process of finding zeros involves setting the function to zero and using factoring techniques, such as the grouping method and zero product property. The tutorial also covers solving equations involving differences of squares and discusses the concept of multiplicity for the zeros found.

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

• Rises left and rises right

• Falls left and rises right

• Rises left and falls right

• Falls left and falls right

Which method is used to factor a polynomial with four terms?

• Synthetic division

• Grouping method

• Completing the square

• Long division

What is the result of factoring the expression x^6 - 4x^4 - 9x^2 + 36 using the grouping method?

• (x^3 - 2)(x^3 + 2)

• (x^2 - 3)(x^2 + 3)

• (x^2 - 4)(x^4 - 9)

• (x^2 + 4)(x^4 + 9)

What are the real zeros of the polynomial x^6 - 4x^4 - 9x^2 + 36?

• x = ±1, ±sqrt(3)

• x = ±2, ±sqrt(3)

• x = ±3, ±sqrt(2)

• x = ±2, ±sqrt(5)

What is the multiplicity of the zeros found in the polynomial x^6 - 4x^4 - 9x^2 + 36?

• Multiplicity of 1

• Multiplicity of 4

• Multiplicity of 3

• Multiplicity of 2