Exploring Polynomial End Behavior and Degree Identification

This video tutorial by Houston Math Prep explains how to identify the end behavior of polynomials from equations and graphs. It covers determining the degree and lead coefficient of polynomials, using this information to sketch end behavior diagrams, and analyzing polynomial graphs to infer degree and lead coefficient. The video provides examples with different polynomials, illustrating how to determine whether the degree is even or odd and whether the lead coefficient is positive or negative.

What is the highest power of X in a polynomial called?

• Multiplier

• Degree

• Lead coefficient

• Constant term

In the polynomial 5x^4 + 3x^2 + 7, what is the lead coefficient?

• 7

• 3

• 5

• 4

For a polynomial with a positive lead coefficient and an even degree, what is the end behavior?

• Down on both sides

• Up on the left, down on the right

• Down on the left, up on the right

• Up on both sides

What is the end behavior of the polynomial -2x^3 + x^2 - 5?

• Down on the left, up on the right

• Up on the left, down on the right

• Down on both sides

• Up on both sides

If a polynomial has an odd degree and a negative lead coefficient, what is the end behavior?

• Down on both sides

• Down on the left, up on the right

• Up on both sides

• Up on the left, down on the right

In the polynomial x^5 - 4x^3 + 2, what is the degree?

• 3

• 4

• 2

• 5

How do you determine the lead coefficient from a polynomial equation?

• It is the sum of all coefficients

• It is the coefficient of the term with the highest power of X

• It is the constant term

• It is the highest power of X

What does the end behavior of a polynomial with an even degree and a negative lead coefficient look like?

• Down on the left, up on the right

• Up on the left, down on the right

• Down on both sides

• Up on both sides

When looking at a polynomial graph, how can you tell if the degree is odd?

• The end behavior is opposite on both sides

• The graph crosses the x-axis

• The graph has a maximum point

• The end behavior is the same on both sides

If a polynomial graph has end behavior going up on the right, what can be inferred about the lead coefficient?

• It is positive

• It is negative

• It is undefined

• It is zero