Factoring Out the Greatest Common Factor

Question 1

Is 5(14x + 8) completely factored?

Accepted Answer

no, both terms inside share a factor of 2, so it becomes 10(7x + 4)

Answer

yes, a common factor of 5 has been taken out and nothing is left to remove

Answer

no, both terms inside share a factor of 2, so it becomes 5(7x + 4)

Answer

no, both terms inside share a factor of 2, so it becomes 2(7x + 4)

Question 2

What is the greatest common factor of the terms of 45h^2 - 27h?

Accepted Answer

9h

Answer

9

Answer

h

Answer

3h

Question 3

Factor 54x^3 + 42x^2 completely.

Accepted Answer

6x^2(9x + 7)

Answer

3x^2(18x + 14)

Answer

6x^2(9x)

Answer

6(9x^3 + 7x^2)

Question 4

Is 7k(2k + 3) completely factored?

Accepted Answer

yes, 2 and 3 share no factor beyond 1 and the last term has no k

Answer

no, both terms inside share a factor of 2, so a 2 still has to come out

Answer

no, both terms inside share a factor of k, so another k still has to come out

Answer

no, both terms inside share a factor of 3, so a 3 still has to come out

Question 5

What is the greatest common factor of the terms of 36m^3 - 81m^2?

Accepted Answer

9m^2

Answer

9

Answer

m^2

Answer

3m^2

Question 6

Is 5k(5k + 2) completely factored?

Accepted Answer

yes, 5 and 2 share no factor beyond 1 and the last term has no k

Answer

no, both terms inside share a factor of 5, so a 5 still has to come out

Answer

no, both terms inside share a factor of k, so another k still has to come out

Answer

no, both terms inside share a factor of 2, so a 2 still has to come out

Question 7

What is the greatest common factor of the terms of 144r^2 + 64r?

Accepted Answer

16r

Answer

16

Answer

r

Answer

8r

Question 8

What is the greatest common factor of the terms of 48y^3 - 72y^2?

Accepted Answer

24y^2

Answer

24

Answer

y^2

Answer

12y^2

Question 9

Factor 32h^2 - 40h completely.

Accepted Answer

8h(4h - 5)

Answer

4h(8h - 10)

Answer

8h(4h)

Answer

8(4h^2 - 5h)

Question 10

Factor -10k^3 - 12k^2 completely, taking out a negative common factor.

Accepted Answer

-2k^2(5k + 6)

Answer

-2k^2(5k - 6)

Answer

2k^2(-5k - 6)

Answer

-2(5k^3 + 6k^2)

Question 11

Factor 4a^3 + 3a^2 completely.

Accepted Answer

a^2(4a + 3)

Answer

4a^2(a + 3)

Answer

a^2(4a)

Answer

a^3(4a + 3)

Question 12

Factor 36x^3 - 84x^2 completely.

Accepted Answer

12x^2(3x - 7)

Answer

6x^2(6x - 14)

Answer

12x^2(3x)

Answer

12(3x^3 - 7x^2)

Question 13

Factor 24r^2 + 36r completely.

Accepted Answer

12r(2r + 3)

Answer

6r(4r + 6)

Answer

12r(2r)

Answer

12(2r^2 + 3r)

Question 14

What is the greatest common factor of the terms of 18b^2 - 12b?

Accepted Answer

6b

Answer

6

Answer

b

Answer

3b

Question 15

Factor 54b^2 + 36b completely.

Accepted Answer

18b(3b + 2)

Answer

9b(6b + 4)

Answer

18b(3b)

Answer

18(3b^2 + 2b)

Question 16

Factor 162a^3 + 18a^2 completely.

Accepted Answer

18a^2(9a + 1)

Answer

9a^2(18a + 2)

Answer

18a^2(9a)

Answer

18(9a^3 + a^2)

Question 17

Is 7m(7m + 2) completely factored?

Accepted Answer

yes, 7 and 2 share no factor beyond 1 and the last term has no m

Answer

no, both terms inside share a factor of 7, so a 7 still has to come out

Answer

no, both terms inside share a factor of m, so another m still has to come out

Answer

no, both terms inside share a factor of 2, so a 2 still has to come out

Question 18

Is 4r(3r^2 + 5r) completely factored?

Accepted Answer

no, both terms inside share a factor of r, so it becomes 4r^2(3r + 5)

Answer

yes, 3 and 5 share no factor beyond 1, so nothing is left to remove

Answer

no, both terms inside share a factor of r, so it becomes 4r(3r + 5)

Answer

no, both terms inside share a factor of r, so it becomes 4(3r + 5)

Question 19

What is the greatest common factor of the terms of 42x^3 - 70x^2?

Accepted Answer

14x^2

Answer

14

Answer

x^2

Answer

7x^2

Question 20

Factor -35w^2 - 10w completely, taking out a negative common factor.

Accepted Answer

-5w(7w + 2)

Answer

-5w(7w - 2)

Answer

5w(-7w - 2)

Answer

-5(7w^2 + 2w)

Question 21

What is the greatest common factor of the terms of 12b^2 + 18b?

Accepted Answer

6b

Answer

6

Answer

b

Answer

3b

Question 22

Factor 2p^3 + 5p^2 completely.

Accepted Answer

p^2(2p + 5)

Answer

2p^2(p + 5)

Answer

p^2(2p)

Answer

p^3(2p + 5)

Question 23

What is the greatest common factor of the terms of 84b^2 - 48b?

Accepted Answer

12b

Answer

12

Answer

b

Answer

6b

Question 24

What is the greatest common factor of the terms of 64w^2 - 8w?

Accepted Answer

8w

Answer

8

Answer

w

Answer

4w

Question 25

Factor 36k^2 + 54k completely.

Accepted Answer

18k(2k + 3)

Answer

9k(4k + 6)

Answer

18k(2k)

Answer

18(2k^2 + 3k)

Question 26

Factor 6x^2 + x completely.

Accepted Answer

x(6x + 1)

Answer

6x(x + 1)

Answer

x(6x)

Answer

x^2(6x + 1)

Question 27

Factor 70r^2 + 60r completely.

Accepted Answer

10r(7r + 6)

Answer

5r(14r + 12)

Answer

10r(7r)

Answer

10(7r^2 + 6r)

Question 28

Factor 70x^3 + 50x^2 completely.

Accepted Answer

10x^2(7x + 5)

Answer

5x^2(14x + 10)

Answer

10x^2(7x)

Answer

10(7x^3 + 5x^2)

Question 29

What is the greatest common factor of the terms of 75x^3 - 30x^2?

Accepted Answer

15x^2

Answer

15

Answer

x^2

Answer

5x^2

Question 30

Is 7(4h + 14) completely factored?

Accepted Answer

no, both terms inside share a factor of 2, so it becomes 14(2h + 7)

Answer

yes, a common factor of 7 has been taken out and nothing is left to remove

Answer

no, both terms inside share a factor of 2, so it becomes 7(2h + 7)

Answer

no, both terms inside share a factor of 2, so it becomes 2(2h + 7)

Question 31

Factor 90p^2 - 108p completely.

Accepted Answer

18p(5p - 6)

Answer

9p(10p - 12)

Answer

18p(5p)

Answer

18(5p^2 - 6p)

Question 32

Factor 96k^2 + 108k completely.

Accepted Answer

12k(8k + 9)

Answer

6k(16k + 18)

Answer

12k(8k)

Answer

12(8k^2 + 9k)

Question 33

Factor 70w^2 - 60w completely.

Accepted Answer

10w(7w - 6)

Answer

5w(14w - 12)

Answer

10w(7w)

Answer

10(7w^2 - 6w)

Question 34

Factor 98h^3 - 14h^2 completely.

Accepted Answer

14h^2(7h - 1)

Answer

7h^2(14h - 2)

Answer

14h^2(7h)

Answer

14(7h^3 - h^2)

Question 35

What is the greatest common factor of the terms of 56t^2 - 42t?

Accepted Answer

14t

Answer

14

Answer

t

Answer

7t

Question 36

Factor -49n^3 - 28n^2 completely, taking out a negative common factor.

Accepted Answer

-7n^2(7n + 4)

Answer

-7n^2(7n - 4)

Answer

7n^2(-7n - 4)

Answer

-7(7n^3 + 4n^2)

Question 37

Factor 80w^3 - 16w^2 completely.

Accepted Answer

16w^2(5w - 1)

Answer

8w^2(10w - 2)

Answer

16w^2(5w)

Answer

16(5w^3 - w^2)

Question 38

What is the greatest common factor of the terms of 126y^3 - 162y^2?

Accepted Answer

18y^2

Answer

18

Answer

y^2

Answer

9y^2

Question 39

What is the greatest common factor of the terms of 12m^2 + 54m?

Accepted Answer

6m

Answer

6

Answer

m

Answer

3m

Question 40

What is the greatest common factor of the terms of 105w^3 - 90w^2?

Accepted Answer

15w^2

Answer

15

Answer

w^2

Answer

5w^2

BLASTROOM

BLASTROOM

BLASTROOM

Factoring Out the Greatest Common Factor

Ways to Play

Device Games: Students play on their phones

Blast Go

Zombie Escape

Avalanche

Maze Blast

Cave Climb

Blast Out

Mystery Auction

Tour Guide

Food Truck Rush

Tug of War

Alien Blast

Glacier Rush

Board Games: Teacher-led, projected to the class

Like what you see?

Bug Blast

BlastRace

BlastQuiz

BlastBoard

Seek & Destroy

Mystery Blast

Checkers

Texas Hold 'Em

Da Bomb

Castle Siege

Hot Potato

Market Mayhem

King of the Hill

Bank Heist

Top Corner

Factoring Out the Greatest Common Factor

Ways to Play

Device Games: Students play on their phones

Blast Go

Zombie Escape

Avalanche

Maze Blast

Cave Climb

Blast Out

Mystery Auction

Tour Guide

Food Truck Rush

Tug of War

Alien Blast

Glacier Rush

Board Games: Teacher-led, projected to the class

Like what you see?

More like this

Bug Blast

BlastRace

BlastQuiz

BlastBoard

Seek & Destroy

Mystery Blast

Checkers

Texas Hold 'Em

Da Bomb

Castle Siege

Hot Potato

Market Mayhem

King of the Hill

Bank Heist

Top Corner