Key Features of Polynomials and Fundamental Theorem of Algebra

What is the end behavior for the graph?

• x → ⁻∞, y→ ⁻∞ and

  x→ ∞, y→ ⁻∞

• x → ⁻∞, y→ ∞ and

  x→ ∞, y→ ∞

• x → ⁻∞, y→ ⁻∞ and

  x→ ∞, y→ ∞

• x → ⁻∞, y→ ∞ and

  x→ ∞, y→ ⁻∞

What is the degree of the graphed polynomial?

• 2

• 3

• 4

• 5

How many zeros does this parabola have? 

• 3

• 2

• 0

• 1

What is the end behavior of this graph?

• x → ⁻∞, y→ ⁻∞ and

  x→ ∞, y→ ⁻∞

• x → ⁻∞, y→ ∞ and

  x→ ∞, y→ ∞

• x → ⁻∞, y→ ⁻∞ and

  x→ ∞, y→ ∞

• x → ⁻∞, y→ ∞ and

  x→ ∞, y→ ⁻∞

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 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

• 1

• 3

• 5

• None of the above

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

What does the Fundamental Theorem of Algebra state about the number of complex roots a polynomial equation has?

• At least one

• Exactly as many as its degree

• At most as many as its degree

• None of the above

A polynomial of degree n has

• only 1 zero

• exactly n zeroes

• at most n zeroes

• more than n zeroes