Answer:
a) 7(x + 2)
b) 9(x - 3)
c) 5(2y - 5)
d) 4(2n + 7)
e) -3(x + 9)
f) -6(x - 5)
Step-by-step 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.
[tex]7x+14\\\frac{7}{7}x+\frac{14}{7}\\x+2\\\\7x+14=7(x+2)[/tex]
b)
9x - 27
9: 1, 3, 9
27: 1 3, 9, 27
The greatest common factor here is 9.
[tex]9x-27\\x-3\\9(x-3)[/tex]
c)
10y - 25
10: 1, 2, 5, 10
25: 1, 5, 25
The GCF here is 5.
[tex]10y-25\\2y-5\\5(2y-5)[/tex]
d)
8n + 28
8: 1, 2, 4, 8
28: 1, 2, 4, 7, 14, 28
The GCF here is 4.
[tex]8n+28\\2n+7\\4(2n+7)[/tex]
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.
[tex]-3x-27\\x+9\\-3(x+9)[/tex]
f)
-6x + 30
6: 1, 2, 3, 6
30: 1, 2, 3, 5, 6, 10, 15, 30
The GCF here is 6.
[tex]-6x+30\\-x+5\\6(-x+5)[/tex]
You could also factor out a -6 instead. It doesn't really matter, but I think it looks nicer like this:
[tex]-6(x-5)[/tex]
