Final Exam Review: Unit 2 (Polynomials)

​Unit 2: Polynomials

• Write the equation of a polynomial given the zeros and a point on the graph

• Add, subtract, multiply complex numbers

• Use the Leading Coefficient Test to determine the end behavior of graphs of polynomial functions

• Graph polynomial functions

• Find all zeros of polynomial functions

• Solve polynomial inequalities

​Link to Notes

Multiple Choice

Assuming the scale is 1, where is f(x) > 0?

• [-4, -1] U [2, +oo)
• (-4, -1) U (2, +oo)
• (-oo, -4] U [-1, 2]
• (-oo, -4) U (-1, 2)

Multiple Choice

Assuming the scale is 1, where is f(x) < 0?

• [-4, -1] U [2, +oo)
• (-4, -1) U (2, +oo)
• (-oo, -4] U [-1, 2]
• (-oo, -4) U (-1, 2)

Multiple Choice

Identify the degree of the polynomial and the sign of the leading coefficient 

• Leading Coefficient Positive
  Degree - Even
• Leading Coefficient Positive
  Degree - Odd
• Leading Coefficient Negative
  Degree - Even
• Leading Coefficient Negative
  Degree - Odd

Multiple Choice

Use the Complex Conjugate Root Theorem to state another complex solution.

Given that -2-5i is a root. 

• -2-5i
• -2+5i
• 2+5i
• 5i

Multiple Choice

Which function has this end behavior?

• $$f(x)=-x^2-3x+1$$

• $$f(x)=-x^3+2x^2+3$$

• $$f(x)=x^4+3x^3-4x+1$$

• $$f(x)=x^5-4x^4+2x^2-1$$

Multiple Choice

Use the Complex Conjugate Root Theorem to state another complex solution.

Given that 3+5i is a root. 

• -3+5i
• -3-5i
• -5i
• 3-5i

Multiple Choice

Use the Complex Conjugate Root Theorem to state another complex solution.

Given that -7i is a root. 

• 7i
• -7i+1
• 1-7i
• 1+7i

Multiple Choice

Write in factored form using the following roots.

7, -2i

• (x-7)(x-2i)

• (x-7)(x+2i)(x-2i)

• (x-7)(x+2i)

• (x-7)(x+7)(x-2i)

Multiple Choice

Write in factored form the polynomial with given roots

x= -4 and 3i

• f(x)= (x-4) (x+3i)

• f(x) = (x+4)(x-3i)

• f(x)= (x-4) (x+3i) (x-3i)

• f(x) = (x+4)(x-3i)(x+3i)

Multiple Choice

True or False: All imaginary roots come in pairs.

• True

• False

Multiple Choice

Which of the following would be the correct factored form with roots 2, 5i, and 6?

• (x-6)(x-2)(x+5i)(x-5i)

• (x+6)(x+2)(x+5i)

• (x-6)(x-2)(x-5i)

• (x+6)(x+2)(x-5i)

Multiple Choice

What is the left side of the graph doing?
f(x) = 4x³ + 2x² + 6x + 10

• up 
• down

Multiple Choice

What are the zeros of the polynomial?

• X=5, x=-3(multiplicity of 2)
• x=-3, x=5(multiplicity of 2)
• x=3, x=-5
• x=5

Multiple Choice

What are the zeros of the function $$f\left(x\right)=3x\left(x-4\right)\left(x+5\right)$$  ?

• $$-4,\ 0,\ 5$$  

• $$-4,\ 3,\ 5$$  

• $$-5,\ -3,\ 4$$  

• $$-5,\ 0,\ 4$$  

Multiple Choice

In the function $$p\left(x\right)=3x\left(x-6\right)^4\left(x+4\right)^3\left(x-5\right)^2$$  which zero has a multiplicity of 3?

• $$-4$$  

• $$0$$  

• $$5$$  

• $$6$$  

Multiple Choice

Write the equation of the polynomial shown.

• y =  ^_(x + 2)(x - 1)²
• y = -(x - 2)(x + 1)²
• y = (x - 2)(x + 1)²
• y = -x³

Multiple Choice

Describe the end behavior of
f(x) = -5x⁴ - 2x² + 8

• Left side: Rises  
   Right side: Rises
• Left Side:  Rises
  Right side: Falls
• Left side: Falls
  Right side: Rises
• Left side: Falls
  Right side: Falls

Multiple Choice

What is the y-intercept?
f(x) = -x⁴ + x³ + 5x² + x + 6

• -1
• 1
• 5
• 6