Solving Higher Order Polynomials

Which of the following could be the equation of this graph in factored form? (Careful-pay attention to multiplicity.)

• f(x) = (x-4)(x-1)²(x+2)(x+4)

• f(x) = (x-4)(x+1)²(x+2)(x+4)

• f(x) = (x-4)(x-1)²(x-2)(x+4)

• f(x) = (x+4)(x+1)²(x-2)(x-4)

The polynomial
f(x) = 5x⁴ + 2x³ + 2x − 7 can have, at most, how many solutions?

• 5

• 4

• 3

• 2

Which is true about the equation of the graph shown?

• The function has an Odd degree

• The function has an Even degree

• The function has 5 real zeros

• The function has a positive leading coefficient

What is the end-behavior of the function 
y = x⁶ - 7x⁵ + 7x - 9

• as x-> -∞  f(x) -> ∞
   as x-> ∞  f(x) -> -∞

• as x-> -∞ f(x) -> ∞
   as x-> ∞  f(x) -> ∞

• as x->-∞ f(x) -> -∞
   as x-> ∞   f(x) -> ∞

• as x-> -∞ f(x) -> -∞
   as x-> ∞ f(x) -> -∞

Select polynomial whose zeros and degree are given.
Zeros: – 5(multiplicity of 3), 9(multiplicity of 2), – 2, 4
Degree: 7

• (x + 5)³(x - 9)²
  (x + 2)(x - 4)

• (x + 5)³(x - 9)²
  (x + 2)⁷(x - 4)⁷

• (x + 5)³(x - 9)²(x + 2)

• (x + 5)(x - 9)(x + 2)
  (x - 4)

Which of the following MUST be true about
the graph shown.

• It has a degree of
  exactly 3

• It has a degree of
  AT LEAST 3

• It has a degree of
  AT LEAST 5

• It has a degree
  of exactly 5

Which of the following best suits the statement for the graph shown:
This polynomial
will have an even degree.

• Sometimes

• Always 

• Never

• Cannot be determined

Which of the following best suits the statement for the graph shown:
This polynomial
will have degree 3.

• Sometimes

• Always 

• Never

• Cannot be determined

The function shown in the graph is:

• even

• odd

• neither odd nor even

• both odd and even

What is the end-behavior of the function 
y = -x³ + 6x² + 7x

• as x-> -∞  f(x) -> ∞
   as x-> ∞  f(x) -> -∞

• as x-> -∞ f(x) -> ∞
   as x-> ∞  f(x) -> ∞

• as x->-∞ f(x) -> -∞
   as x-> ∞   f(x) -> ∞

• as x-> -∞ f(x) -> -∞
   as x-> ∞ f(x) -> -∞