Polynomials and Multiplicity

Polynomial equation x⁴ - 4x³ + 5x² - 4x + 4 = 0 has a solution of x = 2.  Is this synthetic division set up correctly in order to find factors of the polynomial?

• yes

• no

(x - 2) divides polynomial function
 f(x) =  x⁴ - 4x³ + 5x² - 4x + 4 two times.  What numbers should be used to set up the second synthetic division if the goal is to factor f(x)?

• 1   -4   5   -4   4

• 1   -2   1   -2

• 2    -4   2   -4

• cannot be determined

This is the correct end behavior model for the function
y = (x - 2)²(x² + 1)

• true

• false

These functions have the same end behavior model: y₁ = 3x⁵ + 2x³ + x - 1    and    y₂ = 3x²(2x³ + 4x + 2)

• true

• false

Which of these describes end behavior for the polynomial y = 3x⁴ + 2x³ - 7?

• a

• b

• c

• d

Which of these describes end behavior for the polynomial y = 3x⁵ + 2x³ - 7?

• a

• b

• c

• d

Which of these polynomials has end behavior described in option c?

•  y= (x² + 3)(x + 2)

• y = -3x(x + 4)³

• y = -3x(x + 2)⁴

• none of these

A polynomial factors as
f(x) = x³(x + 1)²(x - 4). List the zeros of f(x) and their multiplicity.

• 0 multiplicity 3, 1 multiplicity 2, -4 multiplicity 1

• 0 multiplicity 3, -1 multiplicity 2, 4 multiplicity 1

•  1 multiplicity 2, -4 multiplicity 1

•  -1 multiplicity 2, 4 multiplicity 1

You divide the polynomial g(x) by
(x - 3) and obtain a remainder of 9, what is g(3)?

• -3

• 3

• 9

• cannot be determined

What are the zeros with multiplicities?

• -4 multiplicity 1, -8 multiplicity 1, 5 multiplicity 3

• 4 multiplicity 2, 8 multiplicity 3, -5 multiplicity 1

• 4 multiplicity 3, 8 multiplicity 2, -5 multiplicity 1

• -4 multiplicity 2, -8 multiplicity 3, 5 multiplicity 1