Monomial Worksheets

Solutions

1Indicate which of the following expressions are monomials. If it is, indicate the degree and coefficient of the monomial. If it is not, state why it is not a monomial:

13x3

25x−3

33x + 1

4Algebraic Expression

5Algebraic Expression

6Algebraic Expression

7Algebraic Expression

2 Simplify:

12x2y3z + 3x2y3z

22x3 − 5x3 =

33x4 − 2x4 + 7x4 =

42 a2bc3 − 5a2bc3 + 3a2bc3 − 2 a2bc3 =

3Solve:

1(2x3) · (5x3) =

2(12x3) · (4x) =

35 · (2x2y3z) =

4(5x2y3z) · (2y2z2) =

5(18x3y2z5) · (6x3yz2) =

6(−2x3) · (−5x) · (−3x2) =

4 Solve:

1(12x3) : (4x) =

2(18x6y2z5) : (6x3yz2) =

3(36x3y7z4) : (12x2y2) =

4Polynomial Exercise

5Polynomial Exercise

6Polynomial Exercise

5 Solve:

1(2x3)3 =

2(−3x2)3 =

3Polynomial Exercise


 

1

 

Indicate which of the following expressions are monomials. If it is, indicate the degree and coefficient of the monomial. If it is not, state why it is not a monomial:

13x3

Degree: 3, coefficient: 3

2 5x−3

It is not a monomial because the exponent is not a natural number.

33x + 1

It is not a monomial because there is an addition.

4 Algebraic Expression

Degree: 1, coefficient: Algebraic Expression

5 Algebraic Expression

Degree: 4, coefficient: Algebraic Expression

6 Algebraic Expression

It is not a monomial because it does not have a natural exponent.

7 Algebraic Expression

It is not a monomial because the literal part is within a root.


2

Simplify:

12x2y3z + 3x2y3z = 5x2y3z

22x3 − 5x3 = −3x3

33x4 − 2x4 + 7x4 = 8x4

42a2bc3 − 5a2bc3 + 3a2bc3 − 2a2bc3 = −2a2bc3


3

Solve:

1(2x3) · (5x3) = 10x6

2(12x3) · (4x) = 48x4

35 · (2x2 y3z) = 10x2y3z

4(5x2y3z) · (2 y2z2) = 10x2y5z3

5(18x3y2z5) · (6x3yz2) = 108x6y3z7

6(−2x3) · (−5x) · (−3x2) = −30x6


4

Solve:

1(12x3) : (4x) = 3x2

2(18x6y2z5) : (6x3yz2 ) = 3x3yz3

3(36x3y7z4) : (12x2y2) = 3xy5z4

4Algebraic Expression

5Algebraic Expression 4x3y + 3x2y2 − 8x8

6Algebraic Expression


5

Solve:

1(2x3)3 = 23 · (x3)3 = 8x9

2(-3x2)3 = (-3)3 · (x3)2 = −27x6

3Algebraic Expression