Determine the Zeros of a Polynomial by Factoring

The video tutorial explains how to analyze a polynomial function, specifically focusing on the function F(x) = 49 - x^2. It covers writing the function in standard form, determining the degree and leading coefficient, and using these to predict the end behavior of the graph. The tutorial also demonstrates how to find the intercepts by factoring the function using the difference of squares method and applying the zero product property. It further explains the concept of multiplicity and how it affects the graph's behavior at the zeros. The video concludes with a recommendation to explore additional resources on the difference of squares.

What is the degree of the polynomial function F(x) = 49 - x^2?

• 4

• 3

• 2

• 1

How does the leading coefficient affect the end behavior of the graph?

• It influences whether the graph rises or falls.

• It determines the y-intercept.

• It affects the symmetry of the graph.

• It changes the x-intercepts.

Which method is used to find the zeros of the function F(x) = 49 - x^2?

• Completing the square

• Synthetic division

• Quadratic formula

• Difference of squares

What are the zeros of the function F(x) = 49 - x^2?

• x = 0 and x = 49

• x = 7 and x = -7

• x = 0 and x = -49

• x = 49 and x = -49

What does a multiplicity of 1 indicate about the graph at the intercept?

• The graph touches the x-axis but does not cross it.

• The graph has a horizontal asymptote.

• The graph has a vertical asymptote.

• The graph crosses the x-axis.