Fundamental Theory of Algebra

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

• 4

• 5

• 6

• 7

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?

• nth degree polynomial has at least 1 complex solution

• nth degree polynomial always has 2 x-intercepts

• 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

How many possible negatives solutions does the following polynomial have? f(x) = x⁴ - 3x³ - 17x² + 39x -20

• 3 or 1

• 3

• 1

• 2 or 0

How many solutions does the polynomial f(x)=3x⁴ + 5x² - 6x have?

• 4

• 2

• 3

• 5

The nth degree of a polynomial is equal to the number of root that same polynomial has: is a true statement of which theorem?

• Factor Theorem

• Remainder Theorem

• Fundamental Theorem

• All of the above

• None of the above

What did Carl Friedrich Gauss prove at the age of 22?

• The Distribution of Prime Numbers

• The Existence of Infinitely Many Prime Numbers

• The Law of Quadratic Reciprocity

• The Fundamental Theorem of Algebra

Write a cubic polynomial in standard form with roots 3 and 4i

• x³-3x²+16x-48

• x³-8x²-3x+52

• x³+3x²+3x+1

• x³+3x²-16x+48

State the zeros of the polynomial (include multiplicity):
f(x) = (x²+9)(x -1)³(2x + 5)

• -9, 1, -5

• -9, 1 (multiplicity of 3), -5

• ± 3i , 1 (multiplicity of 3), -5∕2

• ± 3i, 1, -5