Free Printable Dividing Polynomials Test

1.

a)

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

b)

$2x^4+4x^2-x$

c)

$x^3-7x+5$

2.

a)

$2x^3+5+\frac{4}{x}$

b)

$2x^3+9$

c)

$2x^4+5x+\frac{4}{x}$

3.

a)

$x+2$

b)

$x-7$

c)

$x+3$

4.

a)

$2x^2-x-5$

b)

$x^2+2x-5$

c)

$3x-5$

5.

a)

$\left(x+2\right)\left(x+2\right)\left(x-1\right)$

b)

$\left(x-1\right)\left(x+1\right)\left(x+2\right)$

c)

$\left(x+2\right)\left(x+2\right)\left(x+2\right)$

6.

a)

-2

b)

6

c)

7

7.

a)

1

b)

7

c)

0

d)

-5

8.

a)

2

b)

9

c)

-3

d)

6

9.

a)

12

b)

-2

c)

4

d)

8

10.

a)

0

b)

2

c)

4

d)

6

11.

a)

2

b)

3

c)

4

d)

5

12.

a)

A

b)

B

c)

C

d)

D

13.

$\frac{x^2+12x+27}{x+9}$

a)

x+3

b)

x+9

c)

x-3

d)

x-9

14.

$\frac{x^2-13x+40}{x-8}$ What is the dividend to following expression?

a)

x-8

b)

$x^2-13x+40$

c)

x+8

d)

$x^2+13x-40$

15.

$\frac{x^2-7x-44}{x+4}$

a)

x-7

b)

x+4

c)

x-11

d)

x+7

16.

$\frac{x^2+x-42}{x-6}$

a)

x+6

b)

x+8

c)

x-6

d)

x+7

17.

$\frac{2x^2+9x+4}{2x+1}$ What is the divisor in the following equation?

a)

$2x^2+9x+4$

b)

x-4

c)

2x+1

d)

2x+4

18.

$\frac{2x^2-15x+7}{x-7}$

a)

x-7

b)

2x-1

c)

2x+7

d)

x-1

19.

$\frac{2x^2+7x-15}{2x-3}$

a)

x+5

b)

2x-3

c)

x-5

d)

2x+15

20.

$\frac{6x^2+17x+5}{2x+5}$

a)

2x-5

b)

6x+1

c)

3x-1

d)

3x+1

21.

$\frac{3x^2+19x-14}{x+7}$

a)

x-7

b)

3x+1

c)

3x-2

d)

x-3

22.

$\frac{12x^2+7x-12}{3x+4}$

a)

4x-3

b)

3x+3

c)

4x-4

d)

2x+4

23.

$\frac{x^2-5x+6}{x-3}$ What is the divisor in the following expression?

(a)

24.

$\frac{x^2-8x+16}{x-4}$ What is the divisor in the following expression?

(a)

25.

What is the degree of the polynomial function
P(x)=3x⁴-7x²-2x⁷-x+4

a)

4

b)

7

c)

2

d)

11

26.

a)

5w² − 4w + 3

b)

12w² − 9w + 6

c)

12w² − 12w + 9

d)

5w² − 12w+ 9

27.

Divide:
(9x² + 6x) ÷ 3x

a)

3x + 2

b)

3x² + 2x

c)

5x²

d)

3x + 6

28.

a)

5p²- 16p

b)

5p + 4

c)

5p - 4

d)

5p + 4p

29.

a)

1/m²

b)

m²

c)

m⁸

d)

1/m⁸

30.

What is the quotient in the following expression?

a)

2x⁸-8x²-28x

b)

2x⁷-2x -7

31.

Divide the polynomial by the monomial.

a)

15x⁹ - 8x³

b)

3x⁶ - 8x³

c)

-5x¹²

d)

3x⁶ - 40x³

32.

(3x + 5)(3x - 5)

a)

3x² - 9

b)

9x² + 9x - 25

c)

9x² - 25

d)

3x² + 9x + 25

33.

Divide the polynomial by the monomial.

a)

15x⁹ - 8x³

b)

3x⁶ - 8x³

c)

-5x¹²

d)

3x⁶ - 40x³

34.

Add to Simplify:
(4x - 2x³) + (5x³ - 4x + 5)

a)

3x³ + 5

b)

3x³ + 8x + 5

c)

3x² + 5

d)

7x³ + 8x + 5

35.

What is the quotient in the following equation?

(a)

36.

a)

3xy²+5y-2

b)

3xy²+5y+2

c)

3xy+5y-2

d)

3xy+5y+2

37.

a)

8x²y³+7x⁴+5y

b)

8x⁶y⁷-7x⁵y⁸-7x⁴y⁵

c)

8x⁶y⁷-7x⁵y⁸-5x⁴y⁵

d)

8x²y³-7xy⁴-5y

38.

What is the quotient of the following expression?

(a)

39.

Divide:

(4x² - 24x + 35) / (2x - 5)

a)

2x - 7

b)

2x - 12

c)

2x + 12

d)

2x + 7

40.

$\left(4x^4-8x^3-3x^2+7x-2\right)\div\left(2x-1\right)$

Use long division to evaluate

a)

$2x^3-3x^2-3x+2$

b)

$2x^3+3x^2+3x+2$

c)

$2x^3-3x^2-3x-2$

d)

$2x^3+2$

41.

(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

42.

Is (x-2) a factor of f(x)= x³-8x²+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.

43.

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

a)

-2

b)

-6

c)

-12

d)

0

44.

What should be the order of the polynomial coefficients if
(3x - 4x³ + 6x⁴ + 1) / (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

45.

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

46.

Synthetic Division only uses the ____________ of a polynomial to divide.

a)

Terms

b)

Numbers (coefficients)

c)

Variables

d)

Numbers and letters

47.

Which would be better to use?

a)

Long division

b)

Synthetic division

48.

Cam divided (x⁴ + 3x² - 4x - 2) by factor of (x-2) using synthetic division. His work is shown above. Which best describes his mistake?

a)

Cam wrote the remainder incorrectly.

b)

Cam did not use a zero place holder for the x³ term.

c)

Cam added instead of subtracting the rows.

d)

Cam should have used -2 as his division since the factor was x-2.

49.

Is (x-4) a factor of (x³ +x² -16x-16)?

a)

YES

b)

NO

50.

(4x² - 24x + 35) ÷ (2x - 5)

a)

2x - 7

b)

2x - 12

c)

2x + 12

d)

2x + 7

51.

(2x³ + 7x² - 6x - 8) ÷ (x + 4)

a)

2x² - x - 2

b)

2x³ - x² - 2x

c)

2x² + 15x + 54 + 208/x+4

d)

2x³ + 15x² + 54x + 208

52.

a)

x - 7

b)

x²- 7

c)

x + 7

d)

x²+ 3x - 54

53.

a)

5p²- 16p

b)

5p + 4

c)

5p - 4

d)

5p + 4p

54.

Divide:
(9x² + 6x) ÷ 3x

a)

3x + 2

b)

3x² + 2x

c)

5x²

d)

3x + 6

55.

Divide the polynomial by the monomial.

a)

15x⁹ - 8x³

b)

3x⁶ - 8x³

c)

-5x¹²

d)

3x⁶ - 40x³

56.

Divide the polynomial by the monomial.

a)

2x⁸-8x²-28x

b)

2x⁸-2x²-7x

c)

8x⁷-8x-28x

d)

2x⁷-2x -7

57.

a)

5p²- 16p

b)

5p + 4

c)

5p - 4

d)

5p + 4p

58.

Divide:

(4x² - 24x + 35) / (2x - 5)

a)

2x - 7

b)

2x - 12

c)

2x + 12

d)

2x + 7

59.

Find the quotient when (21x²- 52x + 32) is divided by (7x - 8).

a)

3x + 4

b)

3x + 3

c)

3x - 4

d)

3x + 2

60.

The area of a rectangular pool table is: x² + 14x +40.

The length is x + 4. What is the width?

a)

x + 8

b)

x + 14

c)

x + 10

d)

x +4

61.

Divide:
(24x + 4) / (6x+1)

a)

4

b)

4 + 4/6x+1

c)

4x + 0

d)

4x

62.

Divide:

(4x² - 24x + 35) / (2x - 5)

a)

2x - 7

b)

2x - 12

c)

2x + 12

d)

2x + 7

63.

Classify

a)

Monomial

b)

Binomial

c)

Trinomial

d)

Polynomial

64.

Classify by degree of polynomial:
3x³ – 6x

a)

Constant

b)

Linear

c)

Quadratic

d)

Cubic

65.

Divide (m²-7m-11) by (m-8).

a)

m+2 R5

b)

m+1 R(-3)

c)

m-4

d)

m-8 R1

66.

What is the degree of the polynomial function
P(x)=3x⁴-7x²-2x⁷-x+4

a)

4

b)

7

c)

2

d)

11

67.

How many real zeros does the polynomial function
P(x) = x³+2x²+9x+18 have?

a)

0

b)

1

c)

2

d)

3

68.

Factor completely:
x⁴ - 16

a)

(x² + 4)(x + 2)(x - 2)

b)

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

c)

(x² - 4)(x² + 4)

d)

(x - 4)(x+ 4)

69.

Factor completely:
6x³ - 27x² - 105x

a)

(6x² + 15x)(x - 7)

b)

3x(2x² - 9x - 35)

c)

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

d)

(2x + 5)(3x² - 21x)

70.

Factor completely:
x³ + 3x² - 4x - 12

a)

(x + 3)(x² - 4)

b)

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

c)

(x² + 4) (x - 3)

d)

(x² + 3)(x - 4)

71.

Factor
x² - 100

a)

(x - 10)(x +10)

b)

(x - 2)(x + 50)

c)

(x - 4)(x + 25)

d)

(x - 1)(x + 100)

72.

Factor
5x²-28x+32

a)

(3x-10)(x+6)

b)

(x-8)(5x-4)

c)

(5x-8)(x-4)

d)

(5x-8)(x+7)

73.

What is the leading coefficient of the following polynomial?
-4x + 7 - 3x³+ 12x²

a)

-4

b)

7

c)

-3

d)

12

74.

Divide (n²+10n+18) by (n+5).

a)

n+4 R2

b)

n-7 R5

c)

n+5 R(-7)

d)

n+1 R0

75.

Divide (4x³-2x²-3) by (2x²-1).

a)

2x-1 R(2x-4)

b)

2x+3 R(x-3)

c)

2x-1 R0

d)

2x+3 R(3x-5)

76.

Divide (2x³+4x²-5) by (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

77.

Factor by grouping
x³ - 4x² -4x + 16

a)

(x+4)(x+2)(x-2)

b)

(x-4)(x² -4)

c)

(x+4)(x² -4)

d)

(x-4)(x-2)(x+2)

78.

Decide if (x-3) is a factor of 3x³+10x²-x-12

a)

Yes, it is a factor

b)

No, it is not a factor

79.

a)

2x³ + 3x + (7/x-4)

b)

2x² + 3x + 8 + (7/x-4)

c)

2x² + 3x + 8

d)

2x² - x + 10 + (6/x-4)

80.

a)

x - 7

b)

x²- 7

c)

x + 7

d)

x²+ 3x - 54

81.

a)

x² + 14x + 8 - (4/x + 2)

b)

x² + 14x + 48

c)

x³ + 8 - (4x/x-2)

d)

x² + 8x + 48

82.

a)

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

b)

x - 8

c)

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

d)

x + 5

83.

a)

2x - 5

b)

x - 4 + (3/4x - 5)

c)

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

d)

2x + 4

84.

Which subject is your favorite?

a)

Science

b)

Social Studies

c)

English

d)

Math

85.

a)

5w² − 4w + 3

b)

12w² − 9w + 6

c)

12w² − 12w + 9

d)

5w² − 12w+ 9

86.

Divide:
(9x² + 6x) ÷ 3x

a)

3x + 2

b)

3x² + 2x

c)

5x²

d)

3x + 6

87.

a)

4y⁶

b)

4y²²

c)

30y⁶

d)

30y²²

88.

Divide the polynomial by the monomial.

a)

15x⁹ - 8x³

b)

3x⁶ - 8x³

c)

-5x¹²

d)

3x⁶ - 40x³

89.

Simplify $\frac{45x^{15}}{9x^{10}}$

a)

$5x^{1.5}$

b)

$36x^5$

c)

$5x^5$

d)

$36x^{1.5}$

90.

$\frac{18y^{6\ }+9y^{4\ }-12y^2}{3y^2}$

a)

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

b)

$15y^{4\ }+6y^2\ -\ 9$

c)

$6y^{4\ }+3y^2-4$

d)

$6y^{3\ }-3y^2\ +4y$

Dividing Polynomials Test

Total questions: 90

Worksheet time: 5hrs 12mins

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