Determine the zeros for a polynomial by factoring

The video tutorial covers the end behavior of polynomial graphs, focusing on even degrees and positive leading coefficients, which result in graphs rising on both ends. It then explains how to find zeros by setting the polynomial equal to zero and solving for x. The tutorial explores factoring techniques, particularly for quadratics, and highlights the significance of perfect square trinomials. Finally, it discusses multiplicity, emphasizing that even multiplicity causes the graph to rebound at the zero.

What does it mean for a polynomial graph if the degree is even and the leading coefficient is positive?

• The graph falls left and falls right.

• The graph rises left and falls right.

• The graph rises left and rises right.

• The graph falls left and rises right.

To find the zeros of a polynomial function, what should you initially set the function equal to?

• The leading coefficient

• 1

• Zero

• Infinity

Which of the following is a characteristic of a perfect square trinomial?

• It cannot be factored.

• It can be factored into two identical binomials.

• It is always a difference of squares.

• It has no real zeros.

What happens to the graph of a polynomial at a zero with even multiplicity?

• The graph has a vertical asymptote.

• The graph crosses the x-axis.

• The graph rebounds at the x-axis.

• The graph becomes undefined.

If a factor of a polynomial is raised to an even power, what can be said about its multiplicity?

• It has an odd multiplicity.

• It has no multiplicity.

• It has an even multiplicity.

• It has a multiplicity of zero.