Polynomial Review

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

Polynomial function f(x) =  x⁴ - 4x³ + 5x² - 4x + 4 is known to have a zero of x = 2 with a multiplicity of 2. Does this mean (x - 2) divides the polynomial twice?

• 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

(x - 2) divides polynomial function
 f(x) =  x⁴ - 4x³ + 5x² - 4x + 4 two times.  Which of these is a complete factorization of f(x)?

• (x - 2)²(x - 1)(x + 1)

• (x - 2)² (x + 1)

• (x - 2)²(x² + 1)

• cannot be determined

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

Factor this expression:
2x³ + 2x² - 24x

• 2x(x + 4)(x - 3)

• 2x(x - 4)(x - 3)

• 2x(x - 4)(x + 3)

• none of these

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

When a polynomial function f(x) is divided by
 (x + 2), the remainder is 0. 
What is f(2)?

• -8

• 8

• 12

• cannot be determined

When setting up this synthetic division, what polynomial is being divided?

• 2x⁴ + 3x² - x + 2

• 2x⁴ + 3x³ - x² + 2

• 2x⁴ - 3x² + x - 2

• cannot be determined