Okay so it's my first year in Algebra 2 and I have no idea what I'm doing on my homework what so ever. We didn't go over it all that well in class and he didn't say anything that was note worthy.

My first set of problems: Factor out the GCF Exponent= E

a) 15x + 35y b) 6yE3 + 12xE2 - 3x c) 14xE2y + 21xyE4


Could someone help explain how I solve these?

I like the way you asked the question so I'll do (a) the hard way but I'm going to change the problem a bit to 20x + 40y:

1) a number is common to everything. The 20 and the 40
2) Lets do it the hard way:
try to divide both numbers by (2). Integer result. Yes (2*10) and (2 *20)
take the 10 and divide by 2 and the 20 and divide by 2
Are both results an integer. Yes. (2 * 2 * 5) and (2 * 2 * 10)
5 is prime, so we can't do any more.
Collect the like terms: (2*2) and (2*2)
Move outside (2*2) (5x +10y)
The GCF is 2*2 or 4

Check work (4*5)x + (4 * 10)y is what we started with

In esscence: Try to divide by 2 as many times as you can with an integer result.
Then try 3 as many times as you can. 4 is covered by 2, so you can ignore that.
Then 5. 6 is covered by 2 and 3. If you notice a pattern we are diving by prme
numbers as many times as we can with an integer result.

Eventually you can play games. If both end in a 5 or zero it's divisable by 5.
If both end in a zero it's divisable by 10.
If one of the numbers is prime, then check to see if the other ones are divisable
by that prime number.

GCF is a fancy word for the biggest expression that's common to both.
The expression could be a number like that example or could be 6x or 6y or
6E2. Later it will get harder and you'll get terms like (6+2x)

Does that help?

I like the way you asked the question so I'll do (a) the hard way but I'm going to change the problem a bit to 20x + 40y:

1) a number is common to everything. The 20 and the 40
2) Lets do it the hard way:
try to divide both numbers by (2). Integer result. yes (2*10) and (2 *20)
take the 10 and divide by 2 and the 20 and divide by 2
Are both results an integer. yes. (2 * 2 * 5) and (2 * 2 * 10)
5 is prime, so we can't do any more.
Collect the like terms: (2*2) and (2*2)
Move outside (2*2) (5x +10y)
The GCF is 2*2 or 4

Check work (4*5)x + (4 * 10)y is what we started with

In esscence: Try to divide by 2 as many times as you can with an integer result.
Then try 3 as many times as you can. 4 is covered by 2, so you can ignore that.
Then 5. 6 is covered by 2 and 3. If you notice a pattern we are diving by prme
numbers as many times as we can with an integer result.

Eventually you can play games. If both end in a 5 or zero it's divisable by 5.
If both end in a zero it's divisable by 10.
If one of the numbers is prime, then check to see if the other ones are divisable
by that prime number.

GCF is a fancy word for the biggest expression that's common to both.
The expression could be a number like that example or could be 6x or 6y or
6E2. Later it will get harder and you'll get terms like (6+2x)

Does that help?

Yes it helped a lot thank you. I just went through the other 6 in a breeze. ^.^