Determine end behavior of a polynomial

The video tutorial explains how to analyze a polynomial function, starting with rewriting it in descending order. It identifies the degree and leading coefficient, and uses the leading coefficient test to determine the end behavior of the polynomial. The tutorial concludes with a formal method for describing end behavior, emphasizing the importance of understanding how the function behaves as x approaches positive and negative infinity.

What is the correct descending order of the polynomial F(x) = 1 - 4x - 6x^3 - 15x^6?

• -4x - 6x^3 - 15x^6 + 1

• -15x^6 - 6x^3 - 4x + 1

• -6x^3 - 15x^6 - 4x + 1

• 1 - 4x - 6x^3 - 15x^6

What is the degree of the polynomial F(x) = -15x^6 - 6x^3 - 4x + 1?

• 5

• 6

• 3

• 4

How does the end behavior of a polynomial with an even degree and a negative leading coefficient behave?

• Falls left, rises right

• Rises left, rises right

• Falls left, falls right

• Rises left, falls right

Which of the following describes the end behavior of F(x) as x approaches positive infinity?

• F(x) approaches negative infinity

• F(x) approaches zero

• F(x) remains constant

• F(x) approaches positive infinity

As x approaches negative infinity, what happens to F(x) in terms of end behavior?

• F(x) remains constant

• F(x) approaches negative infinity

• F(x) approaches zero

• F(x) approaches positive infinity