Polynomial Functions

The degree of the polynomial determines the number of roots.

• True

• False

Write the equation of the polynomial function
zeros: 0, -2, 4
degree: 5   
0 has a multiplicity of 3

• f(x) = x³(x-2)(x+4)

• f(x) = x³(x+2)(x-4)

• f(x) = x²(x-2)(x+4)

• f(x) = x²(x+2)(x-4)

Find all zeros for the polynomial function
Factor by grouping and then set = 0 to find zeros.
P(x) = x³ -3x²-5x+15

• 3, √5 

• 3, √5, -√5

• -3, √5, -√5

• -3, 5i, -5i

Which of the following is a COMPLETE  list of all possible Rational Zeros?
f(x) = 3x³ + 2x² - 6x + 7

• ±1, ±7, ±1/3, ±7/3

• ±1, 7

• ±1, ±3, ±7, ±7/3

• ±1, ±3, ±7, ±1/3, ±7/3

The function shown has:

• Degree two with negative leading coefficient.

• Degree three with negative leading coefficient.

• Degree four with negative leading coefficient.

• Degree four with positive leading coefficient.

What are the linear terms of the polynomial function?

• (x-2)(x-1)(x+1)(x-2)

• (x-2)(x-1)(x+1)(x+2)

• (x-2)(x-1)(x+1)(x+2)(x-4)

• (x-2)(x-1)(x+1)(x+2)(x+4)

Give the equation of the 4th degree polynomial with zeros: 1 with multiplicity 2 and i.

• x² - 4x + 4

• x³ - 4x² + 4x +ix² -4ix + 4i

• x⁴ - 4x³ + 5x²-4x + 4

• x⁴ - 4x³ + 5x²-4x + 4i

Find a polynomial function of degree 3 with zeros 3i and -2.

• P(x) = x³+2x²+9x+11

• P(x) = x³-2x²+9x+18

• P(x) = x³+2x²+9x+18

• P(x) = x²-3ix+2x-6i

Describe the end behavior of
f(x) = 2x² + 6x⁵ + 10x

• Left side:  Rises
  Right side: Rises

• Left side: Falls
  Right side: Rises

• Left side:Rises
  Right side: Falls

• Left side: Falls
  Right side: Falls

(2x³ + 5x² + 9)
÷
(x + 3)

• 2x² - x + 3

• 2x³ - x² + 3x

• 2x² + 11x + 33 + 108/x+3

• 2x² - 5x + 12