Exploring Polynomial End Behavior

The video tutorial introduces polynomials, defining them as expressions with more than two terms and explaining the rules for their formation, such as no division by variables or negative exponents. It provides examples of polynomials and discusses how to order terms in descending order. The tutorial also covers non-polynomial expressions and explains the significance of the degree of a polynomial in determining its end behavior. Finally, it discusses how the leading coefficient affects the direction of the polynomial's arms.

What is a polynomial?

• An expression with negative exponents

• An expression with only one term

• An expression with more than two terms

• An expression with exactly two terms

Which of the following is NOT allowed in a polynomial?

• Positive exponents

• Constant terms

• Whole number exponents

• Negative exponents

Which of the following is a polynomial?

• x^-2 + 3x

• x^2 + x + 1

• 2/x

• 3x^2 + 5x^2 + 7x^2

Why is descending order important in polynomials?

• It makes the polynomial easier to read

• It helps in identifying the highest degree term

• It is required for polynomial subtraction

• It is required for polynomial addition

What does the highest degree test help determine?

• The number of terms in the polynomial

• The end behavior of the polynomial

• The coefficients of the polynomial

• The roots of the polynomial

If a polynomial has an even degree, how do the arms of the polynomial behave?

• They do not have a specific pattern

• They face opposite directions

• They face the same direction

• One arm faces up and the other faces down

How many times can a polynomial of degree 6 cross the x-axis at most?

• 8 times

• 6 times

• 4 times

• 2 times

What is the end behavior of a polynomial with an odd degree?

• Arms face opposite directions

• Arms face the same direction

• Both arms face down

• Both arms face up

What effect does a negative leading coefficient have on the end behavior of a polynomial?

• The right arm faces up

• Both arms face down

• The right arm faces down

• Both arms face up

For an even degree polynomial with a positive leading coefficient, how do the arms behave?

• They do not have a specific pattern

• One arm faces up and the other faces down

• Both arms face up

• Both arms face down