Determine the number of extrema of a polynomial

The video tutorial explains polynomial functions, focusing on extrema and zeros. It covers polynomial expansion, the relationship between polynomial degree and extrema, and the fundamental theorem of algebra. The tutorial emphasizes graphing to understand extrema and zeros, highlighting the importance of multiplicity in determining extrema.

What is the purpose of expressing a polynomial in standard form?

• To simplify calculations

• To identify extrema and zeros

• To make it easier to graph

• To reduce the degree of the polynomial

How does the degree of a polynomial relate to its zeros?

• The degree equals the total number of real and complex zeros

• The degree is unrelated to the number of zeros

• The degree equals the number of real zeros

• The degree is always one less than the number of zeros

What is the maximum number of extrema a polynomial can have?

• Half the degree of the polynomial

• Twice the degree of the polynomial

• One less than the degree of the polynomial

• Equal to the degree of the polynomial

Why is graphing important in determining the number of extrema?

• It helps visualize the polynomial's behavior

• It confirms the polynomial's degree

• It simplifies the polynomial

• It eliminates complex zeros

What does an odd multiplicity at a zero indicate?

• The zero is a local maximum

• The graph crosses the x-axis at the zero

• The zero is not an extrema

• The graph bounces at the zero

How many extrema are identified in the practical example?

• Two

• Three

• Four

• Five

What is the significance of even multiplicity at a zero?

• The graph crosses the x-axis

• The graph bounces at the zero

• The zero is a local minimum

• The zero is a point of inflection