Polynomials Review

End Behavior

100

Give the degree of the polynomial

3x⁴ + 5x³ - 2x +8

4

200

Describe the end behavior of f(x) = 3x²+1

as x --> ∞, f(x) --> ∞

as x --> -∞, f(x) --> ∞

300

Describe the end behavior of f(x) = -x⁴ + x - 1

as x --> ∞, f(x) --> -∞

as x --> -∞, f(x) --> -∞ 

400

Describe the end behavior of f(x) = 6x³ + x - 5

as x --> ∞, f(x) --> ∞ 

as x --> -∞, f(x) --> -∞ 

500

Describe the end behavior of f(x) = -2x⁵ - 4x² + 9x - 6

as x --> ∞, f(x) --> -∞ 

as x --> -∞, f(x) --> ∞ 

Multiplicity

100

Identify the zeros of the polynomial:

f(x) = (x - 1)(x + 3)

x = 1

x = -3

200

Identify the zeros and multiplicity of each for the following polynomial:

f(x) = x(x - 2)(x + 7)

x=0

x = 2, multiplicity 1

x = -7, multiplicity 1

300

Identify the zeros and multiplicity of each for the  following polynomial:

f(x) = (x - 2)²(x - 5)

x = 2, multiplicity 2

x = 5, multiplicity 1

400

Identify the zeros and multiplicity of each for the following polynomial: 

f(x) = (x - 4)³(x + 2)²(x + 3)

x = 4, multiplicity 3

x = -2, multiplicity 2

x = 3, multiplicity 1

500

Identify the zeros, multiplicity of each zero, and state whether the graph crosses or touches at each zero.

f(x) = x³(x + 5)⁴(x - 3)²(x + 1)

x = -5, multiplicity 4, touches

x = -1, multiplicity 3, crosses

x = 3, multiplicity 2, touches

x = -1, multiplicity 1, crosses

Factoring Polynomials

100

Factor:

x² - 16

(x + 4)(x - 4)

200

Factor: 

3x³ + x² + 21x + 7

(3x + 1)(x² + 7)

300

Factor: 

12x² + 20x + 3

(2x + 3)(6x + 1)

400

Factor: 

27x³ + 1

(3x + 1)(9x² - 3x + 1)

500

Factor: 

64x³ - 27

(4x - 3)(16x² + 12x + 9)

Synthetic Division

100

(x³ - 7x² - 8x + 20) / (x + 2)

x² - 9x + 10

200

(x³ + 4x² - 3x - 14) / (x + 2)

x² + 2x - 7

300

(x³ + 5x² - 32x - 64) / (x + 8)

x² - 3x - 8

400

(x³ - 2x² - 51x + 24) / (x-8)

x² +6x - 3

500

(2x³ - 20x² + 40x + 50) / (x - 5)

2x² - 10x - 10

Solving Polynomials

100

Find the solutions of the polynomial:

f(x) = x² + 5x + 6

x = -3

x = -2

200

Find the solutions of the polynomial: 

f(x) = x³ + 2x² - 4x - 8

x = -2

x = 2

x = -2

300

Use synthetic division to find the solutions of the polynomial:

f(x) = x³ +7x² - 7x - 15 ; (x - 1) is a factor

x = 1

x = -5

x = -3

400

Use synthetic division to find the solutions of the polynomial: 

f(x) = x³ + 6x² - 9x - 54   ;  (x - 3) is a factor

x = 3

x = -3

x = -6

500

Use synthetic division to find the zeros of the polynomial:

f(x) = x³ + x² - 27x + 18 ; (x + 6) is a factor

x = -6

x =