Exploring Zeros of Polynomials and Their End Behavior

The video tutorial covers finding zeros of polynomials and determining their multiplicity. It provides examples of setting polynomial factors to zero and solving for x. The tutorial also explains the concept of end behavior in polynomial functions, using graphs and leading terms to determine how functions behave as x approaches infinity or negative infinity.

What is the first step in finding the zeros of a polynomial?

• Set the polynomial equal to zero

• Set each factor equal to zero

• Set the polynomial equal to one

• Set each factor equal to one

If you have the factor (x + 2), what is the zero of this factor?

• x = 0

• x = 3

• x = -2

• x = 2

What does an exponent of 2 on a factor indicate?

• The factor has no multiplicity

• The factor has a multiplicity of 2

• The factor has a multiplicity of 1

• The factor has a multiplicity of 3

What is the zero of the factor (x + 5)?

• x = -5

• x = 5

• x = 6

• x = 0

If a factor has an exponent of 3, what is its multiplicity?

• 4

• 3

• 2

• 1

What is the zero of the factor (x + 3) with an exponent of 3?

• x = 6

• x = 3

• x = 0

• x = -3

As x approaches infinity, what happens to y if the graph goes up?

• y approaches negative infinity

• y approaches zero

• y approaches positive infinity

• y remains constant

What happens to y as x approaches negative infinity if the graph goes down?

• y remains constant

• y approaches negative infinity

• y approaches zero

• y approaches positive infinity

What does a negative leading term indicate about the end behavior as x approaches infinity?

• y approaches zero

• y approaches negative infinity

• y approaches positive infinity

• y remains constant

For an odd degree polynomial with a negative leading term, what happens to y as x approaches negative infinity?

• y approaches negative infinity

• y approaches zero

• y remains constant

• y approaches positive infinity