Exploring Polynomial End Behavior

The video tutorial covers the basics of polynomials, focusing on the leading coefficient and highest degree. It explains how to arrange polynomials in standard form and discusses the impact of positive and negative leading coefficients on graph behavior. The tutorial also explores how even and odd degrees affect the direction of graph arrows, providing visual examples and explanations of end behavior. Key observations include the consistent behavior of graphs with positive or negative coefficients and the directional changes with even or odd degrees.

What are the two main categories discussed in the video for classifying polynomials?

• Leading coefficient and highest degree

• Leading coefficient and constant term

• Highest degree and number of terms

• Constant term and number of terms

In standard form, how should the terms of a polynomial be ordered?

• By the coefficient size

• From least exponent to greatest exponent

• Alphabetically by variable

• From greatest exponent to least exponent

What is the leading coefficient in the polynomial 6x^4 + 3x^3 + 2x^2 + x + 5?

• 4

• 6

• 1

• 5

If the leading coefficient of a polynomial is positive and the highest degree is even, what is the behavior of the graph?

• Left arrow points up, right arrow points down

• Both arrows point down

• Both arrows point up

• Left arrow points down, right arrow points up

What does the end behavior of a polynomial describe?

• The degree of the polynomial

• The value of the leading coefficient

• The direction of the graph as x approaches positive and negative infinity

• The number of terms in the polynomial

For a polynomial with a positive leading coefficient and an odd highest degree, how does the graph behave?

• Left arrow points down, right arrow points up

• Both arrows point up

• Left arrow points up, right arrow points down

• Both arrows point down

What happens to the graph of a polynomial if the leading coefficient is negative and the highest degree is even?

• Both arrows point up

• Left arrow points up, right arrow points down

• Both arrows point down

• Left arrow points down, right arrow points up

How does the graph behave if the leading coefficient is negative and the highest degree is odd?

• Left arrow points down, right arrow points up

• Both arrows point down

• Left arrow points up, right arrow points down

• Both arrows point up

What is a common characteristic of polynomials with even degrees?

• Their leading coefficients are always negative

• Their graphs always point in the same direction

• Their graphs always point in opposite directions

• Their leading coefficients are always positive

What is a common characteristic of polynomials with odd degrees?

• Their leading coefficients are always positive

• Their graphs always point in the same direction

• Their graphs always point in opposite directions

• Their leading coefficients are always negative