Exploring Polynomials and Their End Behavior

The video tutorial covers the basics of polynomials, including their definition, terms, and examples. It explains how to determine the degree of a polynomial and introduces the concept of the leading coefficient. The tutorial also discusses the end behavior of polynomial graphs, providing a method to predict graph behavior without graphing tools. Key concepts such as odd and even degrees, positive and negative leading coefficients, and their impact on graph behavior are explored.

What is a polynomial?

• An expression with only constant terms

• An expression with no terms

• An expression with more than one term

• An expression with exactly one term

Which of the following is a polynomial?

• x^2

• 2x + 7

• x

• 3

What is the degree of the polynomial X^5 - 3X^2 + 5X?

• 5

• 3

• 2

• 1

If a polynomial is written in the form X^4 - 3X^3 + 2, what is its degree?

• 3

• 2

• 4

• 5

What is the degree of the number 8?

• Undefined

• 8

• 1

• 0

What is the leading coefficient of the polynomial 7X^3 - 3X^2?

• 3

• 7

• -3

• 0

In the polynomial 9X - 3 - 2X^3, what is the leading coefficient?

• 9

• -3

• -2

• 3

What does the end behavior of a polynomial graph describe?

• The middle of the graph

• The start of the graph

• The entire graph

• The end of the graph

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

• Left goes up, right goes down

• Both go down

• Left goes down, right goes up

• Both go up

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

• Both go down

• Left goes up, right goes down

• Left goes down, right goes up

• Both go up