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Worksheets

Write Polynomial from its zeros

Total questions: 33

Worksheet time: 4hrs 47mins

Name
Class
Date
1.
Find a polynomial function of degree 3 with zeros 3i and -2.
a)
P(x) = x3+2x2+9x+11
b)
P(x) = x3-2x2+9x+18
c)
P(x) = x3+2x2+9x+18
d)
P(x) = x2-3ix+2x-6i
2.

Write the factored form of a function if it has zeros of 2, 3 and -1.

a)

(x-2)(x-3)(x+1)

b)

(x-1)(x-2)(x-3)

c)

(x-1)(x+2)(x+3)

d)

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

3.
How many real zeros does the function have?
a)
None
b)
2
c)
3
d)
4
4.
Select polynomial whose zeros and degree are given.
Zeros: – 5(multiplicity of 3), 9(multiplicity of 2), – 2, 4.
a)
(x + 5)3(x - 9)2(x + 2)(x - 4)
b)
(x + 5)3(x - 9)2(x + 2)7(x - 4)7
c)
(x + 5)3(x - 9)2(x + 2)
d)
(x + 5)(x - 9)(x + 2)(x - 4)
5.

Pick the polynomial that has the factors 3, 2, -2

a)

f(x) = (x - 3)(x - 2)(x + 2)

b)

f(x) = (x + 3)(x + 2)(x - 2)

c)

f(x) = (3x)(2x)(-2x)

d)

f(x) = 3x2 + 2x - 2

6.
A polynomial function with rational coefficients has the follow zeros: -1 + i and √5 . Find all additional zeros.
a)
1 + i
b)
-√5 and 1 - i
c)
-√5 and -1 - i
d)
-1 - i
7.
Given x=5, x =3/2, and x= 5/3...
which of the following is the correct factored form? 
a)
(x-5)(2x-3)(3x-5)
b)
(x+5)(2x+3)(3x-5)
c)
(x-5)(x-3/2)(x-5/3)
d)
(x-5)(3x-2)(5x-3)
8.

Select polynomial whose zeros and degree are given.

Zeros: – 5 with multiplicity of 3, 9 with multiplicity of 2, – 2, and 4.

a)

(x + 5)3(x - 9)2(x + 2)(x - 4)

b)

(x + 5)3(x - 9)2(x + 2)7(x - 4)7

c)

(x + 5)3(x - 9)2(x + 2)

d)

(x + 5)(x - 9)(x + 2)(x - 4)

9.
Select polynomial whose zeros and degree are given.
Zeros: – 5(multiplicity of 3), 9(multiplicity of 2), – 2, 4.
a)
(x + 5)3(x - 9)2(x + 2)(x - 4)
b)
(x + 5)3(x - 9)2(x + 2)7(x - 4)7
c)
(x + 5)3(x - 9)2(x + 2)
d)
(x + 5)(x - 9)(x + 2)(x - 4)
10.
How many zeros should the polynomial function
 P(x) = 3x4+4x-8 have?
a)
1
b)
2
c)
3
d)
4
11.

Write the polynomial in standard form given the following zeros. x = -2, 1, 4

a)

f(x) = (x+2)(x-1)(x-4)

b)

f(x) =x3 - 3x2 - 6x + 8

c)

f(x) = x3 + 8

d)

f(x) = x3 - 3x2 + 8

12.

Write a polynomial as linear factors with the given zeros:


x = -1, √2

a)

f(x) = ( x +1) (x + √2)(x - √2)

b)

f(x) = ( x -1) (x + √2)

c)

f(x) = (x + 1)(x - √2)

d)

f(x) = (x + 1)(x - 2)(x + 2)

13.
Find a polynomial function of degree 3 with zeros 3i and -2.
a)
P(x) = x3+2x2+9x+11
b)
P(x) = x3-2x2+9x+18
c)
P(x) = x3+2x2+9x+18
d)
P(x) = x2-3ix+2x-6i
14.

Pick the polynomial that has the factors 5, -1, 0

a)

f(x) = x(x - 1)(x + 5)

b)

f(x) = (x - 5)(x + 1)

c)

f(x) = x(x + 1)(x - 5)

d)

f(x) = 5x2 - x

15.

Which polynomial is in standard form?

a)

2 + x + 4

b)

x4 + x7

c)

2 + x2 + 3x

d)

2x3 + 3x2 + x + 4

16.

How many terms are there is 2x3 +x2 + 4x + 6

a)

4

b)

2

c)

1

d)

6

17.
Identify the degree of the polynomial and the sign of the leading coefficient, using the graph.
a)
Leading Coefficient Positive
Degree - Even
b)
Leading Coefficient Positive
Degree - Odd
c)
Leading Coefficient Negative
Degree - Even
d)
Leading Coefficient Negative
Degree - Odd
18.
Identify the degree of the polynomial and the sign of the leading coefficient, using the graph.
a)
Leading Coefficient Positive
Degree - Even
b)
Leading Coefficient Positive
Degree - Odd
c)
Leading Coefficient Negative
Degree - Even
d)
Leading Coefficient Negative
Degree - Odd
19.
Identify the degree of the polynomial and the sign of the leading coefficient, using the graph.
a)
Leading Coefficient Positive
Degree - Even
b)
Leading Coefficient Positive
Degree - Odd
c)
Leading Coefficient Negative
Degree - Even
d)
Leading Coefficient Negative
Degree - Odd
20.

One zero in the polynomial x3 - 18x2 + 83x - 66 is 1. What are the other zeros? Hint: Synthetic and factoring

a)

6, 11

b)

3, 22

c)

2, 33

21.

Which of the following would be the correct factored form with roots 2, 5i, and 6?

a)

(x-6)(x-2)(x+5i)(x-5i)

b)

(x+6)(x+2)(x+5i)

c)

(x-6)(x-2)(x-5i)

d)

(x+6)(x+2)(x-5i)

22.
Use the Complex Conjugate Root Theorem to state another complex solution. Given that -2-5i is a root. 
a)
-2-5i
b)
-2+5i
c)
2+5i
d)
5i
23.

Write the polynomial with the given zeros

a)

A

b)

B

c)

C

d)

D

24.

Write the polynomial with the given zeros

a)

A

b)

B

c)

C

d)

D

25.
Write a polynomial function of least degree with integral coefficients that has the given zeros.
a)
A
b)
B
c)
C
d)
D
26.

Write a polynomial function of least degree with integral coefficients that has the given zeros.

-1, 5, -3+2i

a)

x4+2x3-16x2-82x-69

b)

x4+7x3-16x2-82x-65

c)

x4+2x3-16x2-82x-65

d)

x4+2x3-16x2-82x-68

27.

Write a polynomial function of least degree with integral coefficients that has the given zeros.

5, -2i

a)

x3-5x2+4x-20

b)

x3-5x2+4x-23

c)

x3-5x2+4x-19

d)

x3-10x2+4x-20

28.

Build a Polynomial with the following Zeros:

-1, 4

a)

x2 - 3x - 4

b)

x2 + 3x + 4

c)

x2 - 5x + 5

d)

x2 - 5x - 4

29.

Build a Polynomial with the following Zeros:

-2, -1, 2

a)

2x3 - x2 - 4x - 2

b)

x3 + 2x2 - 2x + 4

c)

x3 + x2 - 4x + 4

d)

x3 - x2 - x + 4

30.

Build a Polynomial with the following Zeros:

4, 5, 6, 7

a)

x4 - 22x3 + 89x2 + 638x + 730

b)

x4 - 12x3 - 179x2 - 638x + 540

c)

x4 - 22x3 + 179x2 - 638x + 840

d)

x4 - 13x3 + 179x2 - 638x + 640

31.

Identify the Graph of the Polynomial with the following Zeros:

-3, 0, 6

a)
b)
c)
d)
32.

Identify the Graph of the Polynomial with the following Zeros:

-4, -1, 1, 4

a)
b)
c)
d)
33.

Find a polynomial function of degree 4 with zeros 3i and -√2.

a)

x4 - 7x2 + 18

b)

x4 + 7x2 - 18

c)

x4 - 7x2 - 18

d)

x4 + 7x2 + 18