Free Printable Polynomial long/synthetic division

1.

Identify the missing term to complete the solution.

a)

4

b)

-4

c)

5

d)

-5

2.

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

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)

$2x^3+2$

3.

a)

This is correct

b)

This is incorrect

4.

Is this division problem worked correctly?

a)

This is correct!

b)

This is incorrect!

5.

a)

4x - 2

b)

4x + 2

c)

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

d)

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

6.

$\left(2x^3-5x^2-4x-25\right)\div\left(x-4\right)$

a)

$2x^2+3x+8+\frac{-57}{x-4}$

b)

$2x^2-13x-56$

c)

$2x^2+3x+8+\frac{7}{x-4}$

d)

$2x^2-3x-16+-\frac{-89}{x-4}$

7.

What is the quotient when (10n²- 37n - 12) is divided by (n - 4)?

a)

(10n - 3)

b)

(3n - 10)

c)

(10n + 3)

d)

(3n + 10)

8.

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

a)

0

b)

-3

c)

9

d)

5

9.

The "68" in this problem represents the:

a)

remainder

b)

quotient

c)

dividend

d)

divisor

10.

The "2" in this problem represents the:

a)

remainder

b)

quotient

c)

dividend

d)

divisor

11.

Which number represents the quotient?

a)

965

b)

15

c)

5

d)

193

12.

a)

x - 7

b)

x²- 7

c)

x + 7

d)

x²+ 3x - 54

13.

2x³ - 5x² + 3x + 7 ÷ x - 2

a)

2x³ - x² + x + 9

b)

2x² - x + 1

c)

2x² - x + 1 + 9/x-2

d)

2x² - 9x - 15 - 23/x-2

14.

2x³ + 5x² + 9 ÷ x + 3

a)

2x² - x + 3

b)

2x³ - x² + 3x

c)

2x² + 11x + 33 + 108/x+3

d)

2x² - 5x + 12

15.

3x³ + 5x - 1 ÷ x + 1

a)

3x³ - 3x² + 8x - 9

b)

3x² - 3x + 8 - 9/x+1

c)

3x² + 3x + 8 + 7/x+1

d)

3x³ + 3x² + 8x + 7

16.

a)

2x³ + 3x + (7/x-4)

b)

2x² + 3x + 8 + (7/x-4)

c)

2x² + 3x + 8

d)

2x² - x + 10 + (6/x-4)

17.

$\left(2x^3-5x^2-4x-25\right)\div\left(x-4\right)$

a)

$2x^2+3x+8+\frac{-57}{x-4}$

b)

$2x^2-13x-56$

c)

$2x^2+3x+8+\frac{7}{x-4}$

d)

$2x^2-3x-16+-\frac{-89}{x-4}$

18.

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

a)

-2

b)

-6

c)

-12

d)

0

19.

What is the remainder of (3x³ -5x² -4x +1) ÷ (x + 3)?

a)

-25

b)

25

c)

113

d)

-113

20.

Find the Quotient
(2x³ - 5x² - 3x + 7) / (x - 2)

a)

2x²- 9x +15

b)

2x² - x - 5

c)

2x² - 9x - 21

d)

2x² + x + 5

21.

Find the quotient of the polynomials.

$\left(3d^2-4d+13\right)\div\left(d+3\right)$

a)

$3d-13+\frac{52}{d+3}$

b)

$3d-13+\frac{-26}{d+3}$

c)

$3d+5+\frac{-26}{d+3}$

d)

$d-13+\frac{26}{d+3}$

22.

(27x³+ 9x²- 3x - 10) ÷ (3x - 2)

a)

9x⁴+5

b)

9x²+9x+5

c)

9x²-9x+5

d)

9x²-9x

23.

(4x² - 24x + 35) ÷ (2x - 5)

a)

2x - 7

b)

2x - 12

c)

2x + 12

d)

2x + 7

24.

(v³-8v²-25v-8)÷(v+2)

a)

v²-10v-7, R 5

b)

v²-10v-4, R 5

c)

v²-10v-5, R -2

d)

V²-10v-5, R 2

25.

(x³-8x²+6x+41)÷(x-4)

a)

x²-4x-7, R 2

b)

x²-4x-11, R 1

c)

x²-2x-12, R 3

d)

x²-4x-10, R 1

26.

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

27.

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

28.

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

29.

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.

30.

The answer to a division problem is known as the...?

a)

product

b)

sum

c)

difference

d)

quotient

31.

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

a)

0

b)

-3

c)

9

d)

5

32.

Dani is solving the problem below. She set up and solved the synthetic division problem correctly (look at picture). What is the proper way for her to write the answer? $\left(2x^4-9x^3-21x^2+88x+48\right)\div\left(x-4\right)$

a)

$2x^3+x^2+25x+12$

b)

$2x^4+x^3+25x^2+12x\ +0$

c)

$2x^3-x^2-25x-12$

d)

$2x^4-x^3-25x^2-12x\ -0$

33.

$\left(x^3-10x^2+27x-18\right)\div\left(x-3\right)\$

a)

$x^2-7x+6$

b)

$x^2+7x\ -6$

c)

$x^2-3x\ +\ 9$

d)

$x^2+3x\ -\ 9$

34.

$\left(x^3-x^2-x-2\right)\div\left(x-2\right)$

a)

$x^2-5x-4$

b)

$x^2+2x+6$

c)

$x^2+x+1$

d)

$2x^2+x+2$

35.

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

36.

(2x³ - 5x² + 3x + 7) ÷ (x - 2)

a)

2x³ - x² + x + 9

b)

2x² - x + 1

c)

2x² - x + 1 + 9/x-2

d)

2x² - 9x - 15 - 23/x-2

37.

(3x³ - 2x² - 7x + 6) ÷ (x + 1)

a)

3x³ - 5x² - 2x + 8

b)

3x² + x - 6

c)

3x² - 5x - 2 + 8/x+1

d)

3x³ + x² - 6x

38.

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

39.

If you were dividing x⁶ + 4x³ + 2, how many 0's would you need when setting up the top row of your synthetic division?

a)

0

b)

2

c)

4

d)

6

40.

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

a)

0

b)

1

c)

2

d)

3

41.

(3x³ + 5x - 1) ÷ (x + 1)

a)

3x³ - 3x² + 8x - 9

b)

3x² - 3x + 8 - 9/x+1

c)

3x² + 3x + 8 + 7/x+1

d)

3x³ + 3x² + 8x + 7

42.

(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

43.

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

44.

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.

45.

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

46.

What would be the coefficients we use to solve:

$\frac{\left(5x^7+3x^6-9x^4+4x^3+2x-37\right)}{x+1}$

a)

$5,\ \ 3,-9,\ \ 4,\ \ 2,-37$

b)

$5,\ \ 3,\ \ 0,-9,\ \ 4,\ \ 0,\ \ 2,-37$

c)

$5,\ \ 3,\ \ 0,-9,\ \ 4,\ \ 2,-37$

d)

$5,\ \ 3,\ \ 0,-9,\ \ 4,\ \ 2$

47.

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

48.

What is the next step in synthetic division?

a)

Bring the 6 down

b)

Multiply the 9 and 6

c)

Bring the 9 down

d)

Add the 9 and 6

49.

What is the next step in synthetic division?

a)

Multiply the 9 and 6

b)

Add the 9 and 6

c)

Bring down the -48

50.

What is the next step in synthetic division?

a)

Add the -48 to the 54

b)

Multiply the 54 and 6

c)

Divide the 54 by 6

d)

Bring down the -58

51.

What is the next step in synthetic division?

a)

Multiply the 9 and 6

b)

Add the 6 and -58

c)

Bring down the -58

d)

Divide the -58 by 6

52.

It's time to write the answer. What goes in the yellow area?

a)

$n-9$

b)

9

c)

-9

d)

$6n^2-48n-58$

53.

Find the quotient:

(3x³ + 5x - 1) ÷ (x + 1)

a)

3x³ - 3x² + 8x - 9

b)

3x² - 3x + 8 - 9/x+1

c)

3x² + 3x + 8 + 7/x+1

d)

3x³ + 3x² + 8x + 7

54.

Find the quotient:

(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

55.

Find the quotient:

(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

56.

What does it mean to be a factor of a number?

a)

Divides evenly with a remainder of zero.

b)

Divides unevenly with a remainder of 1.

57.

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

58.

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

a)

0

b)

-3

c)

9

d)

5

59.

(2x³ - 5x² + 3x + 7) ÷ (x - 2)

a)

2x³ - x² + x + 9

b)

2x² - x + 1

c)

2x² - x + 1 + 9/x-2

d)

2x² - 9x - 15 - 23/x-2

60.

(2x³ + 5x² + 9) ÷ (x + 3)

a)

2x² - x + 3

b)

2x³ - x² + 3x

c)

2x² + 11x + 33 + 108/x+3

d)

2x² - 5x + 12

61.

(2x³ + 5x² + 9) ÷ (x + 3)

a)

2x² - x + 3

b)

2x³ - x² + 3x

c)

2x² + 11x + 33 + 108/x+3

d)

2x² - 5x + 12

62.

(3x³ - 2x² - 7x + 6) ÷ (x + 1)

a)

3x³ - 5x² - 2x + 8

b)

3x² + x - 6

c)

3x² - 5x - 2 + 8/x+1

d)

3x³ + x² - 6x

63.

(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

64.

4x⁴+4x³-9x²-x+2 ÷ x-1

a)

4x³+8x²-7x-2

b)

4x³+19x²-x-2

c)

4x³+8x²-x-9

d)

4x³+8x²-x-2

65.

(2x³ + 5x² + 9) ÷ (x + 3)

a)

2x² - x + 3

b)

2x³ - x² + 3x

c)

2x² + 11x + 33 + 108/x+3

d)

2x² - 5x + 12

66.

(3x³ + 5x - 1) ÷ (x + 1)

a)

3x³ - 3x² + 8x - 9

b)

3x² - 3x + 8 - 9/x+1

c)

3x² + 3x + 8 + 7/x+1

d)

3x³ + 3x² + 8x + 7

67.

(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

68.

x³-3x²-10x+24 ÷ x+3

a)

x²-7x+5

b)

x-8

c)

x²-6x+8

d)

x+9

69.

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

70.

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

71.

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

a)

0

b)

1

c)

2

d)

3

72.

(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

73.

(3x³ + 5x - 1) ÷ (x + 1)

a)

3x³ - 3x² + 8x - 9

b)

3x² - 3x + 8 - 9/x+1

c)

3x² + 3x + 8 + 7/x+1

d)

3x³ + 3x² + 8x + 7

74.

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

a)

118

b)

132

c)

-132

75.

If 𝟐x²+𝟏𝟎 is divided by 𝒙−𝟏, then what is the remainder?

a)

12

b)

0

c)

-12

d)

8

76.

Find the remainder if you divide

(3x³ + 5x - 1) by (x + 1).

a)

9

b)

-9

c)

7

d)

-7

Polynomial long/synthetic division

Total questions: 76

Worksheet time: 9hrs 58mins

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