Understanding Polynomial Functions and Zeros

The video tutorial covers finding zeros and their multiplicities, polynomial long division, and the factor theorem. It explains the rational zeros theorem and its application, discusses complex zeros, and uses synthetic division. The tutorial also covers solving equations, graph analysis, and using sign charts for domain and range analysis.

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

• Set the function equal to zero

• Multiply the function by a constant

• Divide the function by a variable

• Add a constant to the function

How do odd multiplicities affect the graph of a function?

• They cause the graph to become a straight line

• They cause the graph to go through the x-axis

• They cause the graph to touch the x-axis

• They cause the graph to reflect over the y-axis

What is the purpose of using long division in polynomial division?

• To multiply polynomials

• To subtract polynomials

• To find the remainder of the division

• To add polynomials

What does a zero remainder indicate when using the factor theorem?

• The polynomial is a constant

• The polynomial is a factor

• The polynomial is undefined

• The polynomial is not a factor

What is the Rational Zeros Theorem used for?

• To find the rational zeros of a polynomial

• To find the degree of a polynomial

• To find the imaginary zeros of a polynomial

• To find the coefficients of a polynomial

How can synthetic division help in solving equations?

• By factoring the equation

• By simplifying the equation

• By multiplying the equation

• By dividing the equation

What is the significance of the x-intercept in graphing rational functions?

• It indicates where the graph crosses the y-axis

• It indicates where the graph crosses the x-axis

• It indicates the slope of the graph

• It indicates the maximum point of the graph

What is the purpose of a sign chart in solving inequalities?

• To graph the function

• To find the maximum and minimum points of the function

• To find the zeros of the function

• To determine the sign of the function over intervals