Exploring Multiplicity and End Behavior in Polynomials

What is the primary focus of this video?

• Understanding features of polynomials

• Exploring calculus concepts

• Learning about trigonometric functions

• Solving linear equations

What does multiplicity refer to in polynomials?

• The number of terms in a polynomial

• A repeated zero or root

• The leading coefficient

• The degree of the polynomial

How do you find x-intercepts of a polynomial?

• Set the polynomial equal to one

• Set each factor with a variable equal to zero

• Find the derivative of the polynomial

• Integrate the polynomial

What does the zero product property state?

• If a product of factors equals zero, at least one of the factors must be zero

• The sum of the factors must be zero

• The product of the factors must be one

• The factors must be positive

What happens to the graph at a zero with even multiplicity?

• It creates a hole

• It forms a cusp

• It touches or bounces off the x-axis

• It crosses the x-axis

How does an odd multiplicity affect the graph at a zero?

• The graph crosses the x-axis

• The graph bounces off the x-axis

• The graph forms a horizontal asymptote

• The graph remains constant

What is the end behavior of a polynomial determined by?

• The leading term

• The constant term

• The coefficients of the middle terms

• The number of terms

What is a turning point in a polynomial graph?

• A point where the graph intersects the y-axis

• A point where the graph changes direction

• A point where the graph intersects the x-axis

• A point where the graph becomes undefined

How many turning points can a polynomial of degree n have?

• n

• n+1

• n-1

• n-2

What characteristic do all polynomial graphs share?

• They have asymptotes

• They are continuous with no gaps or cusps

• They are always increasing

• They have sharp points