Determine the Zeros for a Polynomial by Factoring

The video tutorial explains how to determine the end behavior of a polynomial graph based on the exponent and leading coefficient. It then demonstrates finding the zeros of the function by factoring and applying the zero product property. Finally, it discusses the concept of multiplicity and how it affects the graph's behavior at the zeros, indicating whether the graph crosses or touches the x-axis.

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

• Rises left and right

• Falls left and rises right

• Falls left and right

• Rises left and falls right

What is the first step in finding the zeros of the polynomial X^3 + 8X^2 + 16X?

• Factor out the common term X

• Apply the Zero Product Property

• Use the quadratic formula

• Complete the square

After factoring X^3 + 8X^2 + 16X, what is the next step to find the zeros?

• Divide the factors

• Set each factor equal to zero

• Multiply the factors

• Add the factors

What is the multiplicity of the zero at X = 0 for the polynomial X * (X + 4)^2?

• Zero

• One

• Two

• Three

How does the graph behave at a zero with even multiplicity?

• Touches and rebounds at the x-axis

• Oscillates around the x-axis

• Remains constant

• Crosses the x-axis