How to determine end behavior of a polynomial using leading coefficient test

The video tutorial explains how to determine the end behavior of a polynomial by analyzing its degree and leading coefficient. It emphasizes the importance of arranging the polynomial in descending order of powers. The degree, being the highest exponent, and the leading coefficient, whether positive or negative, are crucial in predicting the graph's behavior. For an even degree with a positive leading coefficient, the graph rises to both the left and right. The tutorial concludes with a formal description of end behavior, noting that as x approaches infinity or negative infinity, y also approaches infinity.

What is the first step in determining the behavior of a polynomial?

• Arrange the polynomial in descending order of powers.

• Identify the smallest exponent.

• Find the constant term.

• Arrange the polynomial in ascending order of powers.

What is the degree of a polynomial?

• The sum of all exponents in the polynomial.

• The largest exponent in the polynomial.

• The number of terms in the polynomial.

• The smallest exponent in the polynomial.

How does an even degree and a positive leading coefficient affect the graph of a polynomial?

• The graph is a straight line.

• The graph has no specific direction.

• The graph opens upwards.

• The graph opens downwards.

What happens to the y-values as x approaches negative infinity for a polynomial with an even degree and positive leading coefficient?

• Y-values approach negative infinity.

• Y-values approach zero.

• Y-values remain constant.

• Y-values approach positive infinity.

In the context of polynomial end behavior, what does it mean when x approaches infinity?

• X-values remain constant.

• X-values decrease indefinitely.

• X-values approach zero.

• X-values increase indefinitely.