Question

2. Rewrite each expression by factoring out the greatest common factor.​

Answer 1

a) 7(x + 2)

b) 9(x - 3)

c) 5(2y - 5)

d) 4(2n + 7)

e) -3(x + 9)

f) -6(x - 5)

Explanation:

Factor both numbers and then find the greatest factor that both numbers hav e in common.

a)

7x + 14

7: 1, 7

14: 1, 2, 7, 14

The greatest common factor here is 7. Now, you can factor that out by dividing both numbers by 7 and then multiplying the whole thing by 7 to keep the value equal.

`7x+14\\(7)/(7)x+(14)/(7)\\x+2\\\\7x+14=7(x+2)`

b)

9x - 27

9: 1, 3, 9

27: 1 3, 9, 27

The greatest common factor here is 9.

`9x-27\\x-3\\9(x-3)`

c)

10y - 25

10: 1, 2, 5, 10

25: 1, 5, 25

The GCF here is 5.

`10y-25\\2y-5\\5(2y-5)`

d)

8n + 28

8: 1, 2, 4, 8

28: 1, 2, 4, 7, 14, 28

The GCF here is 4.

`8n+28\\2n+7\\4(2n+7)`

e)

-3x - 27

3: 1, 3

27: 1, 3, 9, 27

The GCF here is 3, but both -3 and -27 also have a common factor of -1. Multiply that with the 3, and you get -3.

`-3x-27\\x+9\\-3(x+9)`

f)

-6x + 30

6: 1, 2, 3, 6

30: 1, 2, 3, 5, 6, 10, 15, 30

The GCF here is 6.

`-6x+30\\-x+5\\6(-x+5)`

You could also factor out a -6 instead. It doesn't really matter, but I think it looks nicer like this:

`-6(x-5)`