Free Printable Polynomials

1.

Which polynomial is written in standard form?

a)

-3x + 8x² + 9x³ - 11

b)

9x³ + 8x²- 3x - 11

c)

8x²+ 9x³ -11 - 3x

d)

-11 - 3x + 8x² + 9x³

2.

Which polynomial is written in standard form?

a)

8x - 11x²

b)

4x³ + 7x - 9

c)

12 + 4x

d)

13x + 7x² - 9x³ + 12

3.

Identify the degree of the monomial:
8a³

a)

8

b)

1

c)

3

d)

11

4.

A polynomial that has two terms is a:

a)

polynomial

b)

monomial

c)

binomial

5.

What is the term classification of the following polynomial?
x³-7x²+3

a)

monomial

b)

binomial

c)

trinomial

d)

polynomial

6.

What is the degree of the polynomial
x²-2x+5

a)

1

b)

2

c)

3

d)

0

7.

4x² + 8x - 7
is classified as a...

a)

Third Degree Monomial

b)

Second Degree Binomial

c)

Second Degree Trinomial

d)

Third Degree Cubic

8.

Identify the degree of the monomial:
8a³

a)

8

b)

1

c)

3

d)

11

9.

Identify the constant term:
4x³ + 2x - 9

a)

4

b)

-2

c)

-9

d)

9

10.

How many terms does this expression have:
-27a³ + 9a² - 45a

a)

what are terms?

b)

0 terms

c)

-45 terms

d)

3 terms

11.

Reorder the following polynomial into Standard Form

$-x^2-15x+7x^4-6+3x^3$

a)

$+7x^4$

b)

$-6$

c)

$-x^2$

d)

$+3x^3$

e)

$-15x$

1)

2)

3)

4)

5)

12.

The following is a (a) Polynomial (by degree)

$-5x^4-2x^3+7x^2-1$

13.

Classify this polynomial by its degree and number of terms.

x² + 6

a)

Linear polynomial

b)

Quadratic trinomial

c)

Quadratic binomial

d)

Cubic binomial

14.

The following polynomial is written in standard form:
7x³ - 11x² + 8x - 5

a)

True

b)

False

15.

The largest exponent which is shown in a polynomial.

a)

exponent

b)

cubic

c)

degree

d)

linear

16.

What is the degree of

f\left(x\right)=3x^3-2x^2+5x-1

a)

4

b)

3

c)

-1

d)

x

17.

How many solutions does the equation

0=4x^2+2x-1

have?

a)

0

b)

1

c)

2

d)

3

18.

How many zeros does the function

g\left(x\right)=x^4-8x-2

have?

a)

3

b)

1

c)

0

d)

4

19.

how many zeros does the function

f\left(x\right)=x\left(x-2\right)\left(x+1\right)

have?

a)

0

b)

1

c)

2

d)

3

20.

how many zeros does the function

h\left(x\right)=x\left(x+3\right)^2\left(x+5\right)

have?

a)

4

b)

2

c)

1

d)

3

21.

f is a polynomial with real coefficients and

2-i

is a zero of f, what is another solution of f(x)?

a)

-2 - i

b)

-2 + i

c)

2 + i

d)

2 - i

22.

g is a polynomial function with real coefficients and

-2i

is a zero of g. What is another zero?

a)

1-2i

b)

1+2i

c)

2i

d)

-2i

23.

f is a polynomial function with real coefficients. If

2-\sqrt{5}i

is a zero of f, what is another zero of f?

a)

$2+\sqrt{5}i$

b)

$2-\sqrt{5}i$

c)

$-2-\sqrt{5}i$

d)

$-2+\sqrt{5}i$

24.

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

25.

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

26.

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

a)

4

b)

2

c)

3

d)

5

27.

A polynomial function has a zero at 4 (multiplicity 3) and 0 (multiplicity 1). Write a function that could represent this function.

a)

$f\left(x\right)=x\left(x-4\right)^3$

b)

$f\left(x\right)=x\left(x+4\right)^3$

c)

$f\left(x\right)=\left(x-4\right)^3$

d)

$f\left(x\right)=x^3\left(x-4\right)^4$

28.

What is the effect on the graph if a zero has a multiplicity of 4?

a)

cross

b)

bounce

c)

wiggle (change direction)

29.

What is the effect on the graph if a zero has a multiplicity of 1?

a)

cross

b)

bounce

c)

wiggle (change direction)

30.

What is the effect on the graph if a zero has a multiplicity of 5?

a)

bounce

b)

cross

c)

wiggle (change direction)

31.

How many real zeros does the function have?

a)

None

b)

2

c)

3

d)

4

32.

What are the zeros for the given polynomial? (Check all that apply)

a)

-4

b)

-3

c)

-2

d)

-1

e)

2

33.

What is the y-intercept?
f(x) = -x⁴ + x³ + 5x² + x + 6

a)

-1

b)

1

c)

5

d)

6

34.

What is the domain of the graph?

a)

[ -∞, ∞]

b)

(-∞,∞)

c)

[-3 , 3]

d)

[-15, 9]

35.

f(x) = (x-4)²(x+1)

a)

Even Degree
- Leading Coeff.

b)

Even Degree
+ Leading Coeff.

c)

Odd Degree
- Leading Coeff.

d)

Odd Degree
+ Leading Coeff.

36.

f(x) = (x+2)(x-3)²(x-4)

Which choice best describes the zeros?

a)

-2, 3 (multiplicity 2), 4

b)

-2 (multiplicity 2), 3, 4

c)

2, -3 (multiplicity 2), -4

d)

2 (multiplicity 2), -3, -4

37.

State the Range.

a)

y ≤ 3

b)

y ≥ 3

c)

All Reals

d)

y ≤ 0

38.

What are the increasing intervals?

a)

(- ∞, -1) & (-1, 0) & (0, 1) & (1, ∞)

b)

(3, 4) & (3, 8)

c)

(- ∞, -1) & (1, ∞)

d)

(-1, 0) & (1, ∞)

39.

At which Zero does the graph cross?

a)

-2

b)

1

c)

3

40.

At which Zero does the graph bounce?

a)

-2

b)

1

c)

3

41.

At which Zero does the graph wiggle?

a)

-2

b)

1

c)

3

42.

What factor would give a zero of -2?

a)

x-2

b)

x+2

43.

What factor would give a zero of 1?

a)

x-1

b)

x+1

44.

What factor would give a zero of 3?

a)

x-3

b)

x+3

45.

What is the leading coefficient of this polynomial?

a)

-5

b)

7

c)

9

d)

10

46.

What is the degree of this polynomial? REMEMBER - add the degrees of each factor

a)

3

b)

9

c)

6

d)

12

47.

What is the degree of this polynomial?

a)

4

b)

7

c)

12

d)

2

48.

What is the degree of this polynomial?

a)

1

b)

2

c)

5

d)

6

49.

Describe the end behavior of the graph.

a)

x → -∞, f(x) → ∞ and x→∞, f(x) →⁻∞

b)

x → -∞, f(x) → ∞ and x→∞, f(x) →∞

c)

x → -∞, f(x) → ∞ and x→∞, f(x) → 0

d)

x → -∞,f(x) → -∞and x→ ∞, f(x) → ∞

50.

In the above graph complete the following end behavior:

As x --> -∞, f(x) --> ____

As x --> +∞, f(x) --> ____

a)

-∞

b)

+∞

-∞

c)

-∞

+∞

d)

+∞

51.

a)

4x - 2

b)

4x + 2

c)

4x - 2 + (1/3x - 1)

d)

4x + 2 + (1/3x - 1)

52.

Is this division problem worked correctly?

a)

This is correct!

b)

This is incorrect!

53.

What should you add to this problem?

(2x³ + 5x² + 9) ÷ (x + 3)

a)

0x⁴

b)

0x³

c)

0x²

d)

0x

54.

a)

2x - 4

b)

2x + 4

c)

2x - 1 + -16/4x-5

d)

2x - 4 + -40/4x-5

55.

(4x² - 24x + 35) ÷ (2x - 5)

a)

2x - 7

b)

2x - 12

c)

2x + 12

d)

2x + 7

56.

a)

This is correct

b)

This is incorrect

57.

(27x³+ 9x²- 3x - 10) ÷ (3x - 2)

a)

9x⁴+5

b)

9x²+9x+5

c)

9x²-9x+5

d)

9x²-9x

58.

What is the remainder when a³ - 4 is divided by a+2?

a)

-2

b)

-6

c)

-12

d)

0

59.

$\frac{5x^2+5x-26}{x+3}$

a)

$5x-10+\frac{4}{x+3}$

b)

$5x-13+\frac{8}{x+3}$

c)

$5x-12+\frac{1}{x+3}$

d)

$5x-10+\frac{5}{x+3}$

60.

$\frac{2x^3+5x^2+0x+9}{x+3}$

a)

$2x^2+3$

b)

$2x^2-x+3+\frac{9}{x+3}$

c)

$2x^2-x+3$

d)

$2x^2-x+3+\frac{18}{x+3}$

61.

$\frac{8x^2+6x-20}{4x-5}$

a)

$2x+4-\frac{40}{4x-5}$

b)

$2x+4$

c)

$2x-1-\frac{16}{4x-5}$

d)

$2x-4$

62.

$\left(9x^3\ -\ 15x^2+27x\right)\div3x$

a)

$3x^2-5x+9$

b)

$3x-5$

c)

$3x^3+5x+9$

d)

$3x^2+5x+9$

63.

What is an expression of more than two algebraic terms?

a)

Monomial

b)

Binomial

c)

Polynomial

d)

Multiplication

64.

What is the answer after we divide on number by another?

a)

Polynomial

b)

Dividend

c)

Quotient

d)

Divisor

65.

True/False:

You must place each term in the quotient directly above its counterpart in the dividend.

a)

True

b)

False

66.

$\left(12x^2-16x-4\right)\div4$

a)

$3x^2+4x-1$

b)

$3x^2-4x$

c)

$3x^2-4x-1$

d)

$4x$

67.

$\left(25x^3-5x\right)\div5x$

a)

$5x^3-x^2$

b)

$5x^2-1$

c)

$5x^2+1$

d)

$5x-1$

68.

What is the remainder when x⁴ - 5 is divided by x + 3?

a)

76

b)

81

c)

7

69.

What is the remainder of (4x³ - 3x² - 4x +2) ÷ (x - 3)?

a)

-71

b)

71

c)

145

70.

What is the remainder of (x³ - 5x² - 8x +1) ÷ (x + 1)?

a)

-13

b)

1

c)

3

71.

If f(x) = 5x² ─ 7x ─10, find the value of f (5) using synthetic division.

a)

150

b)

80

c)

70

72.

What is the remainder when (x¹³ + 10) is divided by (x + 1)?

a)

9

b)

10

c)

11

73.

What is the remainder when (5x²⁰ – 19) is divided by (x ─ 1)?

a)

81

b)

14

c)

- 14

74.

Given P(x) = x³ + x² – x ─ 9, what is the value of P (4)?

a)

14

b)

-53

c)

67

75.

What is the remainder when n³ - 7 is divided by n + 5 ?

a)

118

b)

132

c)

-132

76.

What the remainder after x³ - 2x² - 5x + 6 is divided by x - 3

(a)

77.

What the remainder after x³ - 2x² - 5x + 6 is divided by x - 1

(a)

78.

What is the remainder of (4x³ - 3x² - 4x +2) ÷ (x - 3)?

a)

-71

b)

71

c)

145

79.

Let f(x) = 3x² - 9x +2.
Is k = -3 a zero of the function?

a)

yes

b)

no

80.

Let f(x) = 4x² -33x -27. Is k = 9 a zero of the function?

a)

yes

b)

no

81.

x³-3x²-10x+24 ÷ x+3

a)

x²-7x+5

b)

x-8

c)

x²-6x+8

d)

x+9

82.

Use synthetic division:
(2x³ - 5x - 7) ÷ (x - 2)

a)

2x³ - 4x² + 3x - 13

b)

2x³ + 4x² +3x - 1

c)

2x² - 4x + 3 - 13/x-2

d)

2x² + 4x + 3 - 1/x-2

83.

For synthetic division, what would be the number in the left hand box?

a)

0

b)

1

c)

2

d)

3

84.

Use synthetic division

a)

x - 7

b)

x²- 7

c)

x + 7

d)

x²+ 3x - 54

85.

Is $(x-2)$ a factor of $f(x)=x^3-8x^2+14x-4$ ?

a)

Yes, (x-2) is a factor.

There is a remainder.

b)

No, (x-2) is not a factor.

The remainder is zero.

c)

Yes, (x-2) is a factor.

The remainder is zero.

d)

No, (x-2) is not a factor.

There is a remainder.

86.

Divide using synthetic division $(2x^3+4x^2-5)\div(x+3)$

a)

2x² + 2x - 4 R(-12)

b)

2x² - 2x + 6 R(-23)

c)

2x² - 2x + 8 R(-20)

d)

2x² - 4x + 1 R0

87.

If 𝒙²+𝟑𝒙+𝟕 is divided by 𝒙+𝟐, then what is the remainder?

a)

0

b)

-3

c)

9

d)

5

88.

What should be the correct order of the coefficients when setting up synthetic division for $(3x-4x3+6x4+1)\div(x+3)$ ?

a)

3 0 -4 6 1

b)

6 -4 3 1 0

c)

6 -4 0 3 1

d)

-6 4 0 -3 -1

89.

If you were dividing $x^6+4x^3+2$ , how many 0's would you need as placeholders when setting up the top row of your synthetic division?

a)

0

b)

2

c)

4

d)

6

90.

What is the proper way to write the answer for the following problem?

a)

2x³-x²-25x+12

b)

2x⁴-x³-25x²-12x+0

c)

2x³-x²-25x-12

d)

2x⁴-x³-25x²-12x-0

91.

If you are missing an exponent in your polynomial you must put a zero as a coefficient place holder for that exponent

a)

True

b)

False

92.

Give the correct name for
2x³+5x

a)

Linear Binomial

b)

Cubic Binomial

c)

Quadratic Trinomial

d)

Linear Trinomial

93.

Let f(x) = 4x² -33x -27. Is k = 9 a zero of the function?

a)

yes

b)

no

94.

For synthetic division, what would be the number in the left hand box?

a)

0

b)

1

c)

2

d)

3

Polynomials

Total questions: 94

Worksheet time: 8hrs 50mins

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