Theorems About Roots of Polynomial Equations

Which of the following is a COMPLETE  list of all possible Rational Zeros?
f(x) = x³ + 2x² - 6x + 8

• ±1, ±8
• ±1, ±2, ±4, ±8
• ±1, ±2, ±4
• 1, 2, 4, 8

Solve by using Rational Root Theorem: 
2x³ - 11x² + 12x + 9 = 0

• -1, 1, 3
• -1, 3/2, 3 
• -1/2, 3, 3
• -1/2, 1, 3

Below are four possible zeros for this polynomial.

Figure out which one "works"

f(x) = x³ + 2x² - 11x - 12

• -3

• -4

• 1

• 6

What is the Degree of this polynomial:
f(x)= x³(x + 3)²(x – 5)

• Degree: 6
• Degree: 5
• Degree: 3
• Degree: 2

Use the Fundamental Theorem of Algebra to state the number of zeros/solutions/roots of the polynomial. 

• A
• B
• C
• D

The Fundamental Theorem of Algebra tell us two things. Which of the options does not come from the Fundamental Theorem of Algebra?

• A nth degree polynomial has at least 1 complex solution
• An nth degree polynomial always has 2 x-intercepts
• A nth degree polynomial has n solutions.

State how many of each type of possible solution the following polynomial has

f(x) = -4x⁴ + x³ +11x² - 4x + 8

• Positive: 3 or 1

  Negative: 1

• Positive: 3

  Negative: 1

• Positive: 1

  Negative: 3 or 1

• Positive: 1

  Negative: 3

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

All imaginary roots comes in pairs.

• True
• False

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)