Free Printable Test: Fundamental Theorem of Algebra

1.

How many roots does the above Polynomial have?

a)

4

b)

5

c)

6

d)

7

2.

All imaginary roots comes in conjugate pairs.

a)

True

b)

False

3.

What is the least degree of the graph of the above polynomial?

a)

3

b)

4

c)

5

d)

Not enough information

4.

What is the degree of this polynomial:

f(x)= x³(x + 3)²(x – 5)

a)

Degree: 6

b)

Degree: 5

c)

Degree: 3

d)

Degree: 2

5.

How many zeros/solutions does the following function have?

f(x)= x⁵- 3x³ + x

a)

8

b)

9

c)

5

d)

3

6.

The degree of the polynomial determines the number of roots.

a)

True

b)

False

7.

Use the Fundamental Theorem of Algebra to state the number of zeros/solutions/roots of the polynomial.

a)

A

b)

B

c)

C

d)

D

8.

Use the Fundamental Theorem of Algebra to state the number of zeros/solutions/roots of the polynomial.

a)

A

b)

B

c)

C

d)

D

9.

The nth degree of a polynomial is equal to the number of root that same polynomial has: is a true statement of which theorem?

a)

Factor Theorem

b)

Remainder Theorem

c)

Fundamental Theorem

d)

All of the above

e)

None of the above

10.

f(x)=(x + 4)(x - 3)(x - 2)

List the zeros for this function.

a)

x= -4, x=3, x= -2

b)

x= -4, x= -3, x=2

c)

x= -4, x= 3, x=2

d)

x=4, x= -3, x= -2

11.

Find the DEGREE:

f(x) = (x - 2)³(x + 1)

a)

1

b)

2

c)

3

d)

4

12.

Given one complex zero use the conjugate root theorem to find another. Zero is 7 - 5i

a)

-7+5i

b)

7-5i

c)

-7-5i

d)

7+5i

13.

Given one complex zero use the conjugate root theorem to find another. Zero is: -12 - 8i

a)

12+8i

b)

-12+8i

c)

12-8i

d)

-12-8i

14.

What is the Fundamental Theorem of Algebra?

a)

The degree of the polynomial determines what the x value will be

b)

The degree of the polynomial tells us how many solutions the polynomial will have.

c)

The number of possible rational zeros

d)

States that a complex number and its conjugate are solutions

15.

a)

This graph has two imaginary roots.

b)

This graph has two real roots.

c)

This graph has one imaginary root.

d)

This graph has one real root.

16.

a)

This graph has two real roots.

b)

This graph has one real root.

c)

This graph has one imaginary root.

d)

This graph has two imaginary roots.

17.

Use the Complex Conjugate Root Theorem to state another complex solution. Given that -7i is a root.

a)

7i

b)

-7i+1

c)

1-7i

d)

1+7i

18.

The largest exponent determines the degree of the polynomial.

a)

True

b)

False

19.

Odd Multiplicities have which of the following effects on the x-axis?

a)

Cross the x-axis at a point of reflection

b)

"Touches" the x-axis

20.

Consider : -2x² + 3x - 4
What is the total number of real roots?
What is the total number of complex roots?

a)

Real: 2 and Complex: 0

b)

Real: 0 and Complex: 2

c)

Real: 1 and Complex: 1

d)

Real: 2 and Complex: 2

21.

What is the conjugate of 2 + √3

a)

2 + √3

b)

2 - √3

c)

-2 + √3

d)

-2 - √3

22.

Use the Complex Conjugate Root Theorem to state another complex solution. Given that 3+5i is a root.

a)

-3+5i

b)

-3-5i

c)

-5i

d)

3-5i

23.

If the there is a turning point on the x-axis, what does that mean about the multiplicity of that zero?

a)

Even

b)

Odd

c)

None

24.

If the graph of a function crosses the x-axis, what does that mean about the multiplicity of that zero?

a)

Even

b)

Odd

c)

None

25.

What are the roots of the polynomial function?
y = (x + 2)(x - 7)³

a)

-2, 7 multiplicity 3

b)

-2, 7, 3

c)

2, -7 multiplicity 3

d)

2, -7, 3

26.

f(x)=(x+4)(x-3)(x-2)
List the zeros for this function.

a)

x = -4, x = 3, x = -2

b)

x = -4, x = 3, x = 2

c)

x = -4, x = -3, x = 2

d)

x = 4, x = 3, x = 2

27.

Factor f(x)= x³ - 2x²-13x - 10 given that
(x - 5) is one factor.

a)

(x- 5)(x - 1)(x - 2)

b)

(x - 5)(x + 2)(x - 2)

c)

(x - 5)(x + 2) (x + 1)

d)

(x - 5)(2x - 13)

28.

The largest exponent determines the degree of the polynomial.

a)

True

b)

False

29.

What is the least degree of the graph of the above polynomial?

a)

3

b)

4

c)

5

d)

Not enough information

30.

If 2i is a zero, then

a)

2i repeats twice

b)

-2i is a zero too

c)

1-2i is a zero too

d)

0+2i is a zero too

31.

What does

i

=

a)

$-1$

b)

$\sqrt{-1}$

c)

$1$

d)

32.

What is the conjugate of

1+2i

a)

$1-2i$

b)

$-1-2i$

c)

$-1+2i$

d)

33.

What does

i^2

=?

a)

$-1$

b)

$1$

c)

$\sqrt{-1}$

d)

34.

How many zero's real or imaginary can a degree 4 function have?

a)

zero, zippo, none, nada

b)

4

c)

3

d)

2

e)

1

35.

What's the conjugate of

-i

a)

$i$

b)

$-i$

c)

$1$

d)

$-1$

36.

If 2+3i is a zero of a polynomial function what must another zero be?

a)

2-3i

b)

2+3i

c)

-2-3i

d)

-2+3i

37.

if the following are zeros of a polynomial function what is the least degree of this polynomial function? zero's are;

i+4i,\ -5-2i\ and\ i

a)

6

b)

3

c)

7

d)

101

38.

If

f\left(3\right)=-2.7

and

f\left(4\right)=0.123

what do you know happens to the graph between the x values of 3 and 4?

a)

The graph crosses the x-axis

b)

the graph crosses the y-axis

c)

this outcome means the graph does not cross the x-axis

d)

this outcome means the graph does not cross the y-axis

39.

if $h\left(w\right)=0$ then we know which of the following

a)

w is a zero of the polynomial function

b)

$w=0$

c)

the graph touches or crosses at w

d)

$\left(x-w\right)$ is a factor of the polynomial function

40.

Determine the zeros and their possible multiplicity; check all that apply

a)

$x=-3;\ multiplicity\ 1$

b)

$x=1;\ multiplicity\ 2$

c)

$x=0,\ multiplicity\ 1$

d)

$x=0;\ multiplicity\ 2$

e)

$x=1;\ multiplicity\ 1$

41.

How many zeros does the following function have?
f(x)= x⁵- 3x³ + x

a)

8

b)

9

c)

5

d)

3

42.

The degree of the polynomial determines the number of roots.

a)

True

b)

False

43.

Which of these is a possible rational root of the polynomials?

x³ - 6x² - x + 30

a)

0

b)

4

c)

-9

d)

-15

44.

Find the zeros of the polynomial given one factor. Use synthetic division.

a)

X= 3,4,5

b)

x=-3,-4,-5

c)

x=-3,4,5

d)

x= 3, -4, -5

45.

Factor f(x)= x³ - 2x²-13x - 10 given that
(x - 5) is one factor.

a)

(x- 5)(x - 1)(x - 2)

b)

(x - 5)(x + 2)(x - 2)

c)

(x - 5)(x + 2) (x + 1)

d)

(x - 5)(2x - 13)

46.

The largest exponent determines the degree of the polynomial.

a)

True

b)

False

47.

a)

This graph has two imaginary roots because it is a polynomial of degree two.

b)

This graph has two imaginary roots because it has one hump.

c)

This graph has two imaginary roots because it touches the x-axis at two points.

d)

This graph is imaginary because it the graph has shifted up.

48.

What is the least degree of the graph of the above polynomial?

a)

3

b)

4

c)

5

d)

Not enough information

49.

A Polynomial of Degree 6 CAN have the following number of imaginary roots:

a)

1

b)

4

c)

3

d)

8

50.

What is the degree of the following polynomial that has 4 real roots and 2 complex roots?

a)

4

b)

2

c)

8

d)

6

51.

All imaginary roots comes in pairs.

a)

True

b)

False

52.

What is the degree of a polynomial that has roots of -2, 4i and -4i ?

a)

3

b)

4

c)

1

d)

2

53.

Is (x-3) a factor of
(x³- 3x²+ 2x + 2)?

a)

Yes

b)

No

54.

What are the zeros of f(x) = x²+9x+14

a)

2, 7

b)

-2, -7

c)

2, -7

d)

-2, 7

55.

If 2i is a zero, then

a)

2i repeats twice

b)

-2i is a zero too

c)

1-2i is a zero too

d)

0+2i is a zero too

56.

(5p²+5p-26)÷(p+3)

a)

5p-10, R 4

b)

5p-12, R 1

c)

5p-13, R 8

d)

5p-10, R 5

57.

(8p³-38p²-17p+43)÷(p-5)

a)

8p²+2p-7, R 8

b)

8p²+p-9, R 9

c)

8p²+p-5, R 13

d)

8p²+p-10, R 4

58.

(k²+7k-24)÷(k+10)

a)

k-3, R 6

b)

-2, R 11

c)

-4, R 9

d)

-1, R 4

59.

(4x² - 24x + 35) ÷ (2x - 5)

a)

2x - 7

b)

2x - 12

c)

2x + 12

d)

2x + 7

60.

(27x³+ 9x²- 3x - 10) ÷ (3x - 2)

a)

9x⁴+5

b)

9x²+9x+5

c)

9x²-9x+5

d)

9x²-9x

61.

What is the Degree of this polynomial:
f(x)= x³(x + 3)²(x – 5)

a)

Degree: 6

b)

Degree: 5

c)

Degree: 3

d)

Degree: 2

62.

How many zeros does the following function have?
f(x)= x⁵- 3x³ + x

a)

8

b)

9

c)

5

d)

3

63.

Use the Fundamental Theorem of Algebra to state the number of zeros/solutions/roots of the polynomial.

a)

A

b)

B

c)

C

d)

D

64.

Use the Fundamental Theorem of Algebra to state the number of zeros/solutions/roots of the polynomial.

a)

A

b)

B

c)

C

d)

D

65.

Which of these is a possible rational root of the polynomials?

x³ - 6x² - x + 30

a)

0

b)

4

c)

-9

d)

-15

66.

What is the total number of roots for the following equation?
y = 4x⁶ - 12x⁵ - x⁴ + 2x³ - 6x² - 5x + 10

a)

4

b)

5

c)

6

d)

7

67.

How many solutions does the polynomial f(x)=3x⁴ + 5x² - 6x have?

a)

4

b)

2

c)

3

d)

5

68.

Factor f(x)= x³ - 2x²-13x - 10 given that
(x - 5) is one factor.

a)

(x- 5)(x - 1)(x - 2)

b)

(x - 5)(x + 2)(x - 2)

c)

(x - 5)(x + 2) (x + 1)

d)

(x - 5)(2x - 13)

69.

The largest exponent determines the degree of the polynomial.

a)

True

b)

False

70.

All imaginary roots comes in pairs.

a)

True

b)

False

71.

How many complex zeroes (roots) according to the given function below

$3x^2-\ 5x^4-x^5+4x^3-\ 2x\ +\ 6$

{what degree does it has?}

a)

2

b)

3

c)

4

d)

5

72.

How many complex zeroes (roots) according to the given function below

$3x^2-\ 4x^3-\ 2x\ +\ 6$

{what degree does it has?}

a)

1

b)

2

c)

3

d)

4

73.

How many complex zeroes (roots) according to the given function below

$3x^2-\ 5x^4+4x^3-\ 2x\ +\ 6$

{what degree does it has?}

a)

2

b)

3

c)

4

d)

5

74.

How many complex zeroes (roots) according to the given function below

$3x^2+4x^3-\ 2x\ +\ 6$

{what degree does it has?}

a)

2

b)

3

c)

4

d)

5

75.

Determine the best graph for the given function as following

$-x^5+x$

{odd degree and negative leading coefficient}

a)

b)

c)

d)

76.

Determine the best graph for the given function as following

$x^3-x$

{odd degree and positive leading coefficient}

a)

b)

c)

d)

77.

Determine the best graph for the given function as following

$-x^2-x$

{even degree and negative leading coefficient}

a)

b)

c)

d)

78.

Determine the best graph for the given function as following

$x^4-x$

{even degree and negative leading coefficient}

a)

b)

c)

d)

79.

How many complex zeroes (roots) according to the given function below

$-x^3+x$

a)

3

b)

4

c)

5

d)

6

80.

How many complex zeroes (roots) according to the given function below

$x^5-x$

a)

3

b)

4

c)

5

d)

6

81.

How many complex zeroes (roots) according to the given function below

$-x^4+x$

a)

3

b)

4

c)

5

d)

6

82.

How many complex zeroes (roots) according to the given function below

$x^6-x$

a)

3

b)

4

c)

5

d)

6

83.

Determine the best graph for the given function as following

$-x^3+x$

{odd degree and negative leading coefficient}

a)

b)

c)

d)

84.

Determine the best graph for the given function as following

$x^5-x$

{odd degree and negative leading coefficient}

a)

b)

c)

d)

85.

Determine the best graph for the given function as following

$-x^4+x$

{odd degree and negative leading coefficient}

a)

b)

c)

d)

86.

Determine the best graph for the given function as following

$x^6-x$

{odd degree and negative leading coefficient}

a)

b)

c)

d)

87.

Which the following function is matching the give graph

a)

$-x^3+x+x^8$

b)

$-x^3+x\ -x^7$

c)

$-x^3+x-x^6$

d)

$-x^3+x+x^5$

88.

Which the following function is matching the give graph

a)

$-x^3+x+x^8$

b)

$-x^3+x\ -x^7$

c)

$-x^3+x-x^6$

d)

$-x^3+x+x^5$

89.

Which the following function is matching the give graph

a)

$-x^3+x+x^8$

b)

$-x^3+x\ -x^7$

c)

$-x^3+x-x^6$

d)

$-x^3+x+x^5$

90.

Which the following function is matching the give graph

a)

$-x^3+x+x^8$

b)

$-x^3+x\ -x^7$

c)

$-x^3+x-x^6$

d)

$-x^3+x+x^5$

Test: Fundamental Theorem of Algebra

Total questions: 90

Worksheet time: 4hrs 22mins

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