*This Math quiz is called 'Pre-Algebra - Polynomials: Division (Part 1)' and it has been written by teachers to help you if you are studying the subject at middle school. Playing educational quizzes is a fabulous way to learn if you are in the 6th, 7th or 8th grade - aged 11 to 14.*

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A polynomial is two or more monomial numbers that are linked together in an equation by an addition sign (+), subtraction sign (-) or a multiplication sign (x). In this quiz, we will be dealing with dividing a polynomial by a monomial - a number that stands on its own.

Let’s look at the following example of a polynomial divided by a monomial.

15*x*^{2} + 10*x*^{2} + 5*x* ÷ 5*x* [**Note:** This may also be written as (15

Now let’s work the problem.

(15*x*^{2} + 10*x*^{2} + 5*x*) ÷ (5*x*)

15*x*^{2} ÷ 5*x* = 3*x*

10*x*^{2} ÷ 5*x* = 2*x*

5*x* ÷ 5*x* = 1

Solution: 3*x* + 2*x* + 1

[**Note:** When you divide each of the numbers by the monomial, the exponent numbers are subtracted from each other so in the example problem above, looking at 15

(15*x*^{2} + 10*x*^{2} + 5*x*) ÷ (5*x*)

15*x*^{2} ÷ 5*x* = (15 ÷ 5 = 3) and (*x*^{2} - *x* = *x*)

15*x*^{2} ÷ 5*x* = 3*x*

10*x*^{2} ÷ 5*x* = (10 ÷ 5 = 2) and (*x*^{2} - *x* = *x*)

10*x*^{2} ÷ 5*x* = 2*x*

5*x* ÷ 5*x* = (5 ÷ 5 = 1) and (*x* - *x* = 0)

5*x* ÷ 5*x* = 1

__Solution__: 3*x* + 2*x* + 1

As long as you remember that the exponents are subtracted, there is no need to write out each of the steps listed directly above but you can write them out as listed in the first example. However, this longer version should help you to understand the process.

1.

(96*x*^{2} - 36*x*^{2}) ÷ (12*x*)

8*x*^{3} - 3*x*^{3} = 5*x*^{3}

8*x* + 3*x* = 11*x*

8*x* - 3*x* = 5*x*

8*x*^{3} + 3*x*^{3} = 11*x*^{3}

2.

(50*x*^{6} + 30*x*^{5} - 20*x*) ÷ (10*x*)

5*x*^{5} + 3*x*^{4} - 2*x*^{2}

5*x*^{5} + 3*x*^{4} - 2*x*

5*x*^{5} + 3*x*^{4} + 2

5*x*^{5} + 3*x*^{4} - 2

(50*x*^{6} + 30*x*^{5} - 20*x*) ÷ (10*x*)

50*x*^{6} ÷ 10*x* = 5*x*^{5}

30*x*^{5} ÷ 10*x* = 3*x*^{4}

-20*x* ÷ 10*x* = -2

__Solution__: 5*x*^{5} + 3*x*^{4} - 2

Answer (d) is the correct solution. (Did you remember to subtract your exponents?)

50

30

-20

Answer (d) is the correct solution. (Did you remember to subtract your exponents?)

3.

(99*x*^{9} + 72*x*^{4} + 36*x*^{2}) ÷ (9*x*)

11*x*^{10} + 8*x*^{5} + 4*x*^{3}

11*x*^{8} + 8*x*^{3} + 4*x*

11*x*^{8} + 8*x*^{3} + 4*x*^{3}

11*x*^{9} + 8*x*^{4} + 4*x*^{2}

(99*x*^{9} + 72*x*^{4} + 36*x*^{2}) ÷ (9*x*)

99*x*^{9} ÷ 9*x* = 11*x*^{8}

72*x*^{4} ÷ 9*x* = 8*x*^{3}

36*x*^{2} ÷ 9*x* = 4*x*

__Solution__: 11*x*^{8} + 8*x*^{3} + 4*x*

Answer (b) is the correct solution. (Did you remember to subtract your exponents?)

99

72

36

Answer (b) is the correct solution. (Did you remember to subtract your exponents?)

4.

(57*x*^{6} + 111*x*^{5} - 15*x*^{4}) ÷ (3*x*^{4})

19*x*^{2} + 37*x* + 5

19*x*^{2} + 37*x* - 5*x*

19*x*^{2} + 37*x* - 5

19*x*^{2} + 37*x* + 5*x*

(57*x*^{6} + 111*x*^{5} - 15*x*^{4}) ÷ (3*x*^{4})

57*x*^{6} ÷ 3*x*^{4} = 19*x*^{2}

111*x*^{5} ÷ 3*x*^{4} = 37*x*

-15*x*^{4} ÷ 3*x*^{4} = -5

__Solution__: 19*x*^{2} + 37*x* - 5

Answer (c) is the correct solution. (Did you remember to subtract your exponents?)

57

111

-15

Answer (c) is the correct solution. (Did you remember to subtract your exponents?)

5.

(45*x*^{5} + 35*x*^{3}) ÷ (-5*x*)

(-9*x*^{6}) + (-7*x*^{4})

9*x*^{6} + 7*x*^{4}

9*x*^{4} + 7*x*^{2}

(-9*x*^{4}) + (-7*x*^{2})

(45*x*^{5} + 35*x*^{3}) ÷ (-5*x*)

45*x*^{5} ÷ (-5*x*) = -9*x*^{4}

35*x*^{3} ÷ (-5*x*) = -7*x*^{2}

__Solution__: (-9*x*^{4}) + (-7*x*^{2})

*(In order to not confuse anyone between the divide symbol and the negative value of 5, parentheses are placed around the negative value monomial.)*

Answer (d) is the correct solution. (Did you remember to subtract your exponents?)

45

35

Answer (d) is the correct solution. (Did you remember to subtract your exponents?)

6.

4*x*^{2} + 3*x*^{2} + 2

4*x*^{2} + 3*x*^{2} + 2*x*

4*x*^{2} + 3*x* + 2

4*x* + 3*x* + 2*x*

(24*x*^{3} + 18*x*^{2} + 12*x*) ÷ (6*x*)

24*x*^{3} ÷ 6*x* = 4*x*^{2}

18*x*^{2} ÷ 6*x* = 3*x*

12*x* ÷ 6*x* = 2

__Solution__: 4*x*^{2} + 3*x* + 2

Answer (c) is the correct solution. (Did you remember to subtract your exponents?)

24

18

12

Answer (c) is the correct solution. (Did you remember to subtract your exponents?)

7.

(28*x*^{6} + 21*x*^{3} + 14*x*) ÷ (7*x*)

4*x*^{6} + 3*x*^{3} + 2*x*

4*x*^{5} + 3*x*^{2} + 2

4*x*^{5} + 3*x* + 2

4*x* + 3*x*^{2} + 2*x*

(28*x*^{6} + 21*x*^{3} + 14*x*) ÷ (7*x*)

28*x*^{6} ÷ 7*x* = 4*x*^{5}

21*x*^{3} ÷ 7*x* = 3*x*^{2}

14*x* ÷ 7*x* = 2

__Solution__: 4*x*^{5} + 3*x*^{2} + 2

Answer (b) is the correct solution. (Did you remember to subtract your exponents?)

28

21

14

Answer (b) is the correct solution. (Did you remember to subtract your exponents?)

8.

(64*x*^{8} + 40*x*^{6}) ÷ (8*x*^{3})

8*x*^{5} + 5*x*^{3}

8*x*^{5} + 5*x*^{3} + 8*x*^{3}

8*x*^{11} + 5*x*^{9}

8*x*^{24} + 5*x*^{18}

(64*x*^{8} + 40*x*^{6}) ÷ (8*x*^{3})

64*x*^{8} ÷ 8*x*^{3} = 8*x*^{5}

40*x*^{6} ÷ 8*x*^{3} = 5*x*^{3}

__Solution__: 8*x*^{5} + 5*x*^{3}

Answer (a) is the correct solution. (Did you remember to subtract your exponents?)

64

40

Answer (a) is the correct solution. (Did you remember to subtract your exponents?)

9.

(62*x*^{8} + 28*x*^{5}) ÷ (-2*x*^{2})

(-31*x*^{6}) + (-14*x*^{3})

31*x*^{6} + 14*x*^{3}

(31*x*^{6}) - (14*x*^{3})

(-31*x*^{10}) + (-14*x*^{7})

(62*x*^{8} + 28*x*^{5}) ÷ (-2*x*^{2})

62*x*^{8} ÷ (-2*x*^{2}) = -31*x*^{6}

28*x*^{5} ÷ (-2*x*^{2}) = -14*x*^{3}

__Solution__: (-31*x*^{6}) + (-14*x*^{3})

*(In order to not confuse anyone between the divide symbol and the negative value of 2, parentheses are placed around the negative value monomial.)*

Answer (a) is the correct solution. (Did you remember to subtract your exponents?)

62

28

Answer (a) is the correct solution. (Did you remember to subtract your exponents?)

10.

(78*x*^{2} + 52*x*^{2}) ÷ (13*x*^{2})

6*x*^{2} + 4*x*^{2}

6 + 4 = 10

6*x*^{2} + 4*x*^{2} = 10*x*^{4}

6*x*^{4} + 4*x*^{4} = 10*x*^{8}

(78*x*^{2} + 52*x*^{2}) ÷ (13*x*^{2})

78*x*^{2} ÷ 13*x*^{2} = 6

52*x*^{2} ÷ 13*x*^{2} = 4

__Solution__: 6 + 4 = 10

Answer (b) is the correct solution. (Did you remember to subtract your exponents?) In addition, this problem has a final answer of 10 as 6 and 4 are “like” numbers

78

52

Answer (b) is the correct solution. (Did you remember to subtract your exponents?) In addition, this problem has a final answer of 10 as 6 and 4 are “like” numbers

x^{2}- 36x^{2}) ÷ (12x)96

x^{2}÷ 12x= 8x-36

x^{2}÷ 12x= -3xSolution: 8x- 3x= 5xAnswer (c) is the correct solution. (Did you remember to subtract your exponents?) In addition, this problem has a final answer of 5

xas 8xand 3xare “like” numbers