Roots, Zeros and Intercepts of Polynomials

How many positive solutions does the following polynomial have?

f(x) =3x⁵ - x⁴ + 3x² - 6x +11

• 4, 2, or 0

• 4

• 3 or 1

• 3

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

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

Which formula is the Fundamental Theorem of Algebra Formula?

• There are infinitely many rationals between two reals.

• Every polynomial equation having complex coefficents and degree greater than the number 1 has at least one complex root.

• There are infinitely many prime numbers.

• All numbers are rational numbers.

What is the total number of possible negative roots for the following equation? y = 4x⁶ - 12x⁵ - x⁴ + 2x³ - 6x² - 5x + 10

• 4

• 3

• 2

• 5

Find the zeros of the polynomial given one factor.

• X= 3,4,5

• x=-3,-4,-5

• x=-3,4,5

• x= 3, -4, -5

Which best describes the multiplicity of a root?

• It is the number of times the corresponding factor is repeated

• It is the highest degree of the polynomial

• It is the number of times x is multiplied by itself

• It is the number of x-intercepts on a graph

What are the
zeros of the polynomial
y = 3(x + 4)(x + 1)(x - 3)?

• -4, -1, 3

• 3, -3, 4, 1

• 4, 1, -3

• 3, -4, -1, 3

What are the roots of the polynomial function?
y = (x + 2)(x - 7)³

• -2, 7 multiplicity 3

• -2, 7, 3

• 2, -7 multiplicity 3

• 2, -7, 3

How could you determine    if x-2 is a factor of 2x³-5x²+x-2?

• Use synthetic division and see if the quotient is even

• Ask the person sitting next to me

• Use synthetic division and see if the remainder is zero

• Flip a coin