Fundamental Theory of Algebra

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

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

• 0

• 4

• -9

• -15

Find the zeros of the polynomial given one factor. Use synthetic division.

• X= 3,4,5

• x=-3,-4,-5

• x=-3,4,5

• x= 3, -4, -5

Which of the following statements is a direct consequence of the Fundamental Theorem of Algebra?

• Every polynomial of degree greater than zero has at least one real root.

• Every polynomial of degree greater than zero has at least one complex root.

• Every polynomial can be factored into linear factors in the set of real numbers.

• Every polynomial can be factored into linear factors in the set of complex numbers.

What is the Fundamental Theorem of Algebra?

• The degree of the polynomial determines what the x value will be

• The degree of the polynomial tells us how many solutions the polynomial will have.

• The number of possible rational zeros

• States that a complex number and its conjugate are solutions

• 1

• 3

• 5

• None of the above

What statement must be true about the this polynomial?

• It has exactly 3 roots (including repeated roots) and they have to be real numbers

• It has exactly 5 roots (including repeated roots) that may be real or complex numbers

• It has exactly 3 roots (including repeated roots) that may be real or complex numbers

• It has exactly 5 roots (including repeated roots) and they have to be real numbers

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

• 4

• 5

• 6

• 7

Factor f(x)= x³ - 2x²-13x - 10  given that
(x - 5) is one factor.

• (x- 5)(x - 1)(x - 2)

• (x - 5)(x + 2)(x - 2)

• (x - 5)(x + 2) (x + 1)

• (x - 5)(2x - 13)