FACTOR OUT A MONOMIAL WORKSHEET

Factor each completely. 

1)  6x⁴ + 4x³y

2)  12a² - 21ab

3)  6n³ - 3n⁵

4)  10y³ - 9y² + y

5)  15x³ + 10x²y - 25x²z

6)  -8m⁷ + 24m⁶ + 12m⁵

7)  -7u² - 21u³

8)  28m²n² - 12m³n - 20m³n²

9)  8x²- 80x

10) 8x² + 72x

11)  13x³ + 26x² - 39x³

12)  17x² + 34x + 51

13)  18m² n⁴ - 12m² n³ + 24m² n²

14)  10x² + 35x

15)  10x² y - 15 x y²

16)  12x² - 9x + 15

17)  x³ y⁴ + x² y²

18)  18b - 9b²

19)  3x⁵ + 4x⁴ - 5x²

20)   16a⁵ b³ + 32a⁴ b

21)  12x³ + 4x²

Detailed Answer Key

1. Answer :

6x⁴ + 4x³y

Greatest common factor of 6x⁴ and 4x³y is 2x³. 

Divide 6x⁴ and 4x³y by 2x³.

6x⁴/2x³  =  3x

4x³y/2x³  =  2y

Write the quotients 3x and 2y inside the parenthesis and multiply by the greatest common factor 2x³.

2x³(3x + 2y)

So, 

6x⁴ + 4x³y  =  2x³(3x + 2y)

2. Answer :

12a² - 21ab

Greatest common factor of 12a² and -21ab is 3a. 

Divide 12a² and -21ab by 3a. 

12a²/3a  =  4a

-21ab/3a  =  -7b

Write the quotients 4a and -7b inside the parenthesis and multiply by the greatest common factor 3a.

3a(4a - 7b)

So, 

12a² - 21ab  =  3a(4a - 7b)

3. Answer :

6n³ - 3n⁵

Greatest common factor of 6n³ and -3n⁵ is 3n³. 

Divide 6n³ and -3n⁵ by 3n³. 

6n³/3n³  =  2n

-3n⁵/3n³  =  -n²

Write the quotients 2n and -n² inside the parenthesis and multiply by the greatest common factor 3n³.

3n³(2n - n²)

So, 

6n³ - 3n⁵  =  3n³(2n - n²)

4. Answer :

10y³ - 9y² + y

Greatest common factor of 10y³, -9y² and y is y. 

Divide 10y³ and -9y² and y by y. 

10y³/y  =  10y²

-9y²/y  =  -9y

y/y  =  1

Write the quotients 10y², -9y and y inside the parenthesis and multiply by the greatest common factor y.

y(10y² - 9y + 1)

So, 

10y³ - 9y² + y  =  y(10y² - 9y + 1)

5. Answer :

15x³ + 10x²y - 25x²z

Greatest common factor of 15x³, 10x²y, -25x²z is 5x².

Divide 15x³, 10x²y and -25x²z by 5x².

15x³/5x²  =  3x

10x²y/5x²  =  2y

-25x²z/5x²  =  -5z

Write the quotients 3x, 2y and -5z inside the parenthesis and multiply by the greatest common factor 5x².

5x²(3x + 2y - 5z)

So, 

15x³ + 10x²y - 25x²z  =  5x²(3x + 2y - 5z)

6. Answer :

-8m⁷ + 24m⁶ + 12m⁵

Greatest common factor of -8m⁷, 24m⁶ and 12m⁵ is 4m⁵. 

Divide -8m⁷, 24m⁶ and 12m⁵ by 4m⁵. 

-8m⁷/4m⁵  =  -2m²

24m⁶/4m⁵  =  6m

12m⁵/4m⁵  =  3

Write the quotients -2m², 6m and 3 inside the parenthesis and multiply by the greatest common factor 4m⁵.

4m⁵(-2m² + 6m + 3)

So, 

-8m⁷ + 24m⁶ + 12m⁵  =  4m⁵(-2m² + 6m + 3)

7. Answer :

-7u² - 21u³

Greatest common factor of -7u² and -21u³ is -7u².

Divide -7u² and -21u³ by -7u².

-7u²/(-7u²)  =  1

-21u³/(-7u²)  =  3u

Write the quotients 1 and 3u inside the parenthesis and multiply by the greatest common factor -7u².

-7u²(1 + 3u)

So, 

-7u² - 21u³  =  -7u²(1 + 3u)

8. Answer :

28m²n² - 12m³n - 20m³n²

Greatest common factor of 28m²n², -12m³n, -20m³n² is 4m²n.

Divide 28m²n², -12m³n, -20m³n² by 4m²n.

28m²n²/4m²n  =  7n

-12m³n/4m²n  =  -3m

-20m³n²/4m²n  =  -5mn

Write the quotients 7n, -3m and -5mn inside the parenthesis and multiply by the greatest common factor 4m²n.

4m²n(7n - 3m - 5mn)

So, 

28m²n² - 12m³n - 20m³n²  =  4m²n(7n - 3m - 5mn)

9. Answer :

= 8x²- 80x

80 is a product of 8, 80 = 8(10)

Factoring 8 from these two terms, we get

= 8(x² - 10)

10. Answer :

= 8x² + 72x

72 is a product of 8, 72 = 8(9)

Factoring 8 from these two terms, we get

= 8(x² + 9)

11. Answer :

13x³ + 26x² - 39x

Factoring 13x, we get

= 13x (x² + 2x - 3)

Considering the trinomial inside the bracket, that can be factorable.

= 13x (x² + 3x - 1x - 3)

= 13x [x(x + 3) - 1(x + 3)]

= 13x (x - 1) (x + 3)

12. Answer :

= 17x² + 34x + 51

Factoring 17,we get

= 17(x² + 2x + 3)

13. Answer :

= 18m² n⁴ - 12m² n³ + 24m² n²

18 = 6(3)

12 = 6(2)

24 = 6(4)

Factoring 6m² n²

= 6m² n²(3 n² - 2n + 4)

14. Answer :

= 10x² + 35x

= 5x(2x + 7)

15. Answer :

= 10x² y - 15 x y²

Factoring 5 xy, we get

= 5xy(2x - 3y)

16. Answer :

= 12x² - 9x + 15

Factoring 3, we get

= 3(4x² - 3x + 5)

17. Answer :

= x³ y⁴ + x² y²

Factoring x² y², we get

= x² y²(x y² + 1)

18. Answer :

= 18b - 9b²

Factoring 9b, we get

= 9b(2 - b)

19. Answer :

= 3x⁵ + 4x⁴ - 5x²

Factoring x², we get

= x² (3x³ + 4x² - 5)

20. Answer :

= 16a⁵ b³ + 32a⁴ b

Factoring 16a⁴ b, we get

= 16a⁴ b(a b² + 2)

21. Answer :

= 3x² - 10x³ 

Factoring x², we get

= x² (3 - 10x)

22. Answer :

= 12x³ + 4x²

Factoring 4x², we get

= 4x² (3x + 1)

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