Free Printable Division of polynomials

1.

Are you ready?

a)

Yes!

b)

Yes na Yes!

2.

Solve using long division. $\left(x^2+2x\ -\ 63\right)\div\left(x+9\right)$

a)

$x-7$

b)

$x^2-7$

c)

$x+7$

d)

$x^2+3x-54$

3.

Is this division problem worked correctly?

a)

This is correct!

b)

This is incorrect, and error occurs on the 2nd line!

c)

This is incorrect, and the error occurs on the 4th line!

d)

This is incorrect, and the error occurs on the 3rd line!

4.

Which term must be inserted in the dividend before you begin long division?

$\left(2x^3+5x^2+9\right)\div\left(x+3\right)$

a)

$0x^4$

b)

$0x^3$

c)

$0x^2$

d)

$0x$

5.

What is the remainder when you divide
$\left(2x^3-5x-7\right)\ by\ \left(x+2\right)$ ?

a)

-9

b)

11

c)

-13

d)

-1

6.

What do you call the number that you divide by?

a)

Quotient

b)

Divisor

c)

Remainder

d)

Factor

7.

The answer to a division question is called the. . .

a)

Divisor

b)

Multiplier

c)

Quotient

d)

Sum

8.

Which term is missing in this problem?

(2x³ + 5x² + 9 )÷

(x + 3)

a)

x⁴

b)

x³

c)

x²

d)

x

9.

(2x³ - 5x² + 3x + 7) ÷ (x - 2)

a)

2x³ - x² + x + 9

b)

2x² - x + 1

c)

$2x^2-x+1+\frac{9}{x-2}$

d)

$2x^2-9x-15-\frac{23}{x-2}$

10.

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

11.

Find the remainder
(2x³ - 5x - 7) / (x + 2)

a)

-9

b)

11

c)

-13

d)

-1

12.

Use long division to solve: $\left(3y^5+5y^2-12y+10\right)\div\left(y^2+2\right)$

a)

$3y^3+6y^2+5y$

b)

$3y^4-6y^2+5$

c)

$3y^3-6y^2+5y-5$

d)

$3y^3-6y+5$

13.

Use long division to solve: $\left(x^5+12x^2-5x\right)\div\left(x^2-2x+5\right)$

a)

$x^3-2x-1$

b)

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

c)

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

d)

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

14.

Use long division to solve: $\left(4y^3-2y^5+y^6-y^4-4y+2\right)\div\left(y^4+2-2y^2\right)$

a)

$-y^2+2y-1$

b)

$y^2-2y+1$

c)

$y^2+2y-1$

d)

$y^2-2y+2$

15.

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

16.

(2x³ + 5x² + 9) ÷ (x + 3)

a)

2x² - x + 3

b)

2x³ - x² + 3x

c)

2x² + 11x + 33 + 108/x+3

d)

2x² - 5x + 12

17.

$\frac{32m^2+12mn\ -54n^2}{8m\ -\ 9n}$

a)

4m+6n

b)

6m-4n

c)

4m-6n

d)

6m+4n

18.

Simplify.

a)

2n + 2

b)

4n + 2

c)

2n + 4

d)

4n + 4

19.

Simplify.

a)

2x²+ 3x

3

b)

3x² +3x

2

c)

2x²+ 3

3

d)

3x + 3

2

20.

Simplify.

a)

3w³ - 2w + 4

b)

-3w³ - 2w + 4

c)

3w³ + 2w + 4

d)

-3w³ - 2w - 4

21.

Simplify.

a)

x - 3xy + 2

b)

x + 3xy + 2

c)

x - 3xy - 2

d)

-x - 3xy - 2

22.

Use long division algorithm.

a)

4x - 2

b)

4x + 2

c)

2x - 4

d)

2x + 4

23.

Use synthetic division.

a)

b)

c)

d)

24.

Find the quotient of

(4x² - 10x + 3) ÷ (x - 5)

a)

4x - 10 + 52 / x - 5

b)

4x + 10 + 53 / x - 5

c)

4x + 11 + 53 / x + 5

25.

What is the quotient of

(14x ² + 69x + 27) ÷ (7x + 3)?

a)

14x² + 63x

b)

-2x + 9

c)

2x + 9

26.

Find the quotient of

(3x⁴ - 5x² + 14) ÷ (x + 2)

a)

3x³ - 6x² + 7x - 14 + 42 ⁄ x+2

b)

3x³ - 5x² + 7x - 14 + 42 ⁄ x+2

c)

3x³ - 5x² + 7x + 14 + 42 ⁄ x+2

27.

Find the quotient of

(3x² + 6x - 24) ÷ (x + 3)

a)

3x - 3 + 15/x + 3

b)

3x - 3 - 15/x + 3

c)

3x - 3 - 14/x + 3

28.

Find the quotient of

(25x² - 50x + 25) ÷ (5x - 5)

a)

5x - 5

b)

25x² - 50x

c)

5x + 5

29.

What is the remainder of

(25x² - 50x + 25) ÷ (5x - 5) ?

a)

-5

b)

0

c)

5

30.

What is the divisor of

(25x² - 50x + 25) ÷ (5x - 5) ?

a)

0

b)

5x + 5

c)

5x - 5

31.

Find the quotient of (x²+ 4x - 21) ÷ (x + 7)

a)

x - 7

b)

x - 3

c)

x + 3

32.

What is the degree classification of this polynomial?

x²+ 4x -8

a)

binomial

b)

trinomial

c)

quadratic

d)

cubic

33.

What is the term classification of the following polynomial?

x³- 7x² +3

a)

monomial

b)

binomial

c)

trinomial

d)

polynomial

34.

Which is an example of a linear polynomial?

a)

x² - 5

b)

6x + 4

c)

5x⁵

d)

2x³ - 9x²

35.

Which is an example of a cubic binomial?

a)

x³ + 5

b)

x² + 3

c)

x² + 5x - 6

d)

5x³

36.

What is the leading coefficient of the following polynomial?

5x² - 3x + 6

a)

2

b)

-3

c)

5

d)

6

37.

Find the sum (3 - 2x + 2x²) + (4x -5 +3x²)

a)

7x -7x + 5x²

b)

5x²+ 2x - 2

c)

5x²

d)

5x² + 6x +8

38.

Solve. (x+2) (x+3)

a)

x² + 5x + 6

b)

x² + x + 6

c)

x² + 6x + 6

d)

x² + 5x + 5

39.

Simplify 2x (-2x - 3)

a)

-4x - 3

b)

x² - 3

c)

-4x² - 6x

d)

-4x - 6

40.

Classify the polynomial and given degree 5x³y²

a)

Monomial, 3

b)

Uninomial, 3

c)

Uninomial, 5

d)

Monomial, 5

41.

What is the constant of this polynomial? 2x³ - 8x² + 3x - 7

a)

2

b)

-8

c)

3

d)

-7

42.

Classify the polynomial by its number of terms 4x² - 2

a)

monomial

b)

binomial

c)

trinomial

d)

polynomial

43.

Which is an example of a quadratic monomial?

a)

x³ + 5

b)

x² + 3

c)

x² + 5x - 6

d)

-5x²

44.

Simplify (3x²) (3x⁴y³)

a)

9x⁶y³

b)

3x⁶y³

c)

6x⁸y³

d)

6x⁸y⁶

45.

Terms in a polynomial are separate by what?

a)

A. Parenthesis

b)

B. multiplication/division

c)

C. constant

d)

D. addition/ subtraction

46.

Which of the following is a polynomial?

a)

x^½ + 6

b)

x³ + 8 - 3x^-2

c)

1/2 x -3

d)

x⁴ + 8 - 3

47.

(12v² + 18v) ÷ (6v)

a)

3v + 4

b)

7v + 1

c)

2v + 3

d)

6v + 2

48.

(2x² -7x -15) ÷ (x-5)

a)

2x + 3

b)

2x +4

c)

2x +5

d)

2x +6

49.

(x² - 25) ÷ (x+5)

a)

x+4

b)

x-4

c)

x+5

d)

x-5

50.

(x³ + 5x² +10x -8) ÷ (x+2)

a)

x² +3x -4

b)

x² +3x +4

c)

x² -3x -4

d)

x² -3x +4

51.

(6x² +7x -20) ÷ (2x + 5)

a)

3x -4

b)

3x+4

c)

4x -3

d)

4x +3

52.

(x³ +7x² +7x -6) ÷ (x +2)

a)

x² -5x +3

b)

x² -5x -3

c)

x² +5x -3

d)

x² +5x +3

53.

Use either long or synthetic division in finding the quotient and the remainder of the given polynomials. Simplify your answer.

2x+x^3+7x^2-40\div\left(x-2\right)

a)

$x^2-9x+20;\ r=0$

b)

$x^2+9x+20;\ r=0$

c)

$x^2-9x-20;\ r=0$

d)

$x^2-9x+20;\ r=0$

54.

Use either long or synthetic division in finding the quotient and the remainder of the given polynomials. Simplify your answer.

6x^2+x^3+2x+44\div\left(x+2\right)

a)

$x^2+4x-6;\ r=56$

b)

$x^2+4x+6;\ r=56$

c)

$x^2-4x+6;\ r=56$

d)

$x^2-4x-6;\ r=56$

55.

Use either long or synthetic division in finding the quotient and the remainder of the given polynomials. Simplify your answer.

x^3+35+9x^2+13x\div\left(x-5\right)

a)

$x^2+14x+83;\ r=450$

b)

$x^2+14x-83;\ r=450$

c)

$x^2-14x+83;\ r=450$

d)

$x^2-14x-83;\ r=450$

56.

Use either long or synthetic division in finding the quotient and the remainder of the given polynomials. Simplify your answer.

4x^3+26x+320+21x^2\div\left(x+5\right)

a)

$4x^2+x+21\ ;\ r=215$

b)

$4x^2-x+21\ ;\ r=215$

c)

$4x^2+x-21\ ;\ r=215$

d)

$4x^2-x-21\ ;\ r=215$

57.

Use either long or synthetic division in finding the quotient and the remainder of the given polynomials. Simplify your answer.

13x+2x^3-5x^2-15\div\ \left(2x+5\right)

a)

$x^2-5x+6\ ;\ r=-45$

b)

$x^2-5x+6\ ;\ r=45$

c)

$x^2+5x-6\ ;\ r=-45$

d)

$x^2+5x-6\ ;\ r=45$

58.

What is the remainder when you divide $x^2+3x+10\ \div\ \left(x+2\right)?$

(a)

59.

What is the remainder when you divide $10x^3+5x^2+74x-40\ \div\ \left(2x+1\right)?$

(a)

60.

What is the remainder when you divide

12x^3+10x^2+5x+1\ \div\ \left(3x+1\right)?

(a)

61.

The total cost of

\left(3a-2b\right)

units of cell phone is

6a^2+5ab-6b^2

pesos. What expression represents the cost of one cell phone? Use long division to solve for the quotient.

a)

$2a-3b$

b)

$3a-2b$

c)

$a-3b$

d)

$2a+3b$

62.

Simplify $4x^5\ \cdot\ 6x^{10}$

a)

$24x^{15}$

b)

$10x^{15}$

c)

$\sqrt{24x^{15}}$

d)

$\sqrt{10x^{15}}$

63.

Which expression represents the product of $\left(2r\right)\left(r^2+3r\ -\ 7\right)$

a)

$-2r^2-6r\ ^{ }+\ 14$

b)

$2r^2+6r\ ^{ }-\ 14$

c)

$2r^3+6r\ ^2-\ 14r$

d)

$2r^3+6r\ ^2+\ 14r$

64.

Simplify $\frac{x^8}{x^3}$

a)

$x^{24}$

b)

$x^5$

c)

$\frac{1}{x^5}$

d)

$x^{11}$

65.

What is the product of ( 8p + 11 )( 8p - 11 )?

a)

8p² - 22

b)

16p²- 22

c)

64p² - 121

d)

64p² - 88p - 121

66.

Simplify $\frac{3x^2y\ +\ 6xy\ -9x^2y^2}{3xy}$

a)

x -3xy + 2

b)

x -3xy - 2

c)

x + 3xy + 2

d)

-x - 3xy - 2

67.

Simplify $\frac{4x^2-24x\ +\ 35}{2x\ -\ 5}$

a)

7x - 2

b)

2x - 7

c)

7x + 2

d)

2x + 7

68.

What is the remainder when 𝑎³ − 5𝑎² − 𝑎 + 5 is divided by 𝑎 + 2?

a)

-21

b)

-5

c)

5

d)

21

69.

What is the remainder when 𝑥³ + 2𝑥² − 𝑥 + 5 is divided by 𝑥 + 1?

a)

3

b)

5

c)

7

d)

15

70.

Classify by number of terms:
2x – 9

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

71.

Classify by degree of polynomial:
2x – 9

a)

Constant

b)

Linear

c)

Quadratic

d)

Cubic

72.

Classify by degree of polynomial:
12

a)

Constant

b)

Linear

c)

Quadratic

d)

Cubic

73.

Classify the following polynomial

a)

quadratic trinomial

b)

cubic binomial

c)

constant monomial

d)

quadratic binomial

74.

Classify the following polynomial

a)

cubic biniomial

b)

quadratic polynomial

c)

linear binomial

d)

quadratic trinomial

75.

Add the polynomials:
(3x³+3x²–4x+5) + (x³–2x²+x–4)

a)

4x³ + 1x² – 3x + 1

b)

2x³ + 1x² - 5x + 9

c)

6x³ + 1x - 1x² - 3

d)

3x⁵ +1x - 1x⁵ - 3x

76.

Simplify the expression.
(4n⁴-8n+4) - (8n²+4n⁴+1)

a)

-8n² - 8n + 3

b)

-7n² - 8n + 3

c)

-6n²- 8n + 3

d)

-7n² - 4n + 3

77.

Multiply:
(4x+1)(5x−2)

a)

20x² + 3x − 2

b)

20x² − 11x + 5

c)

20x² − 18x + 2

d)

20x² − 3x − 2

78.

Simplify the expression.
-3x²( 7x²- x + 4)

a)

-21x⁴ + 3x³ -12x²

b)

7x² - x + 4 (-3x²)

c)

21x⁴+ 3x³+ 12x²

d)

-12x²+ 3x³-21x⁴

79.

How many terms are in the following polynomial?
3x³ - 2y + 8x -16

a)

1

b)

2

c)

4

d)

-16

80.

Find the area of a rectangle with length (x - 5) and width (3x + 1).

a)

3x²+16x-5

b)

3x²-14x+5

c)

3x²-14x-5

81.

Divide using 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

Division of polynomials

Total questions: 81

Worksheet time: 11hrs 2mins

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