Finding Zeros and Analyzing Polynomial Behavior

The video tutorial explains solving equations by replacing variables and applying the zero product property. It discusses the concept of multiplicity and its impact on graph behavior, such as crossing or bouncing at zeros. The tutorial also covers sketching polynomial graphs by hand, focusing on end behavior and graphing techniques without technology.

What is the first step in solving a polynomial equation?

• Set the equation to zero

• Factor the polynomial

• Graph the polynomial

• Find the degree of the polynomial

Tags

CCSS.HSA-REI.B.4B

What property is applied after setting the polynomial equation to zero?

• Associative Property

• Zero Product Property

• Distributive Property

• Commutative Property

Tags

CCSS.HSA-REI.B.4B

What must be undone first when solving inside the parentheses?

• Addition

• Multiplication

• Cubing and Squaring

• Subtraction

What is the zero of the polynomial when x equals 1?

• x = -1

• x = 1

• x = 2

• x = 0

What does the multiplicity of a zero indicate?

• The degree of the polynomial

• The number of times the zero appears

• The leading coefficient

• The constant term

Tags

CCSS.HSF-IF.C.7C

What happens to the graph at a zero with an odd multiplicity?

• It bounces

• It crosses

• It remains constant

• It shifts

What is the degree of the polynomial if it is expanded from (x - 1)^3 and (x + 2)^2?

• 6

• 7

• 3

• 5

What is the end behavior of a polynomial with an odd degree and a positive leading coefficient?

• Rises left, rises right

• Rises left, falls right

• Falls left, rises right

• Falls left, falls right

Where are the zeros of the polynomial located?

• At x = 1 and x = -2

• At x = 0 and x = 1

• At x = 2 and x = -1

• At x = -1 and x = 2

Tags

CCSS.HSF-IF.C.7C

What does the graph do at x = -2?

• It crosses

• It remains constant

• It shifts

• It bounces