Algebra 2 Rational Root Theorem, Remainder Theorem, Factor Theorem and Fundamental Theorem of Algebra

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

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

How many zeros does the following function have?
f(x)= x⁵ - 3x³ + x

• 8
• 9
• 5
• 3

The degree of the polynomial determines the number of roots.

• True
• False

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

• A
• B
• C
• D

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

• A
• B
• C
• D

What is the total number of possible positive roots for the following equation?

y = 4x⁶ - 12x⁵ - x⁴ + 2x³ - 6x² - 5x + 10

• 4

• 5

• 6

• 7

Which of these is a possible rational root of the polynomials?

x³ - 6x² - x + 30

• 0

• 4

• -9

• -15

Which of these is a possible root of the polynomials?
x³ - 6x² - x + 30

• 0
• 4
• -9
• -15

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.

Which of the following roots match the above polynomial:

• -3,-1,4
• -3,2i,-2i