Anyone with algebra 1+ experience (factoring)

I'm trying to figure out how to factor polynomials. Right now I'm struggling on them in my algebra class. I've asked and asked again on how to factor problems, but I just don't seem to get it. Here are some examples:
6x^3+18x^2

3m^2+24m+36

35xy-60x^2

If you could help me understand how to factor any or all of these, it would be GREATLY appreciated!!

6x^3+18x^2
What does both terms have in common?
They both have 6x^2 in common.
So you divide out 6x^2 from both terms
6x^2 (x+3)
Check your work by multiplying the 6x^2 by what's inside the parenthesis. You'll see that it equals 6x^3 + 18x^2

3m^2+24m+36
What do all terms have in common? 3. So divide 3 out
3(m^2 + 8m + 12)
Now you can either use the quadratic formula, or you can see which two numbers add to 8 and multiply to 12.
The two numbers are 6 and 2.
So you put them in this form: 3(m+6)(m+2)
Again, check your work by multiplying it all together and you'll see that it equals the starting equation.

35xy-60x^2
Again, what do both terms have in common? They both have 5x in common so divide it out.
5x(7y-12x)
There's nothing more you can do so check your work by multiplying it all together and you'll see that it matches the original equation.

I hope this helps you understand. The main technique is first to see if there's any term or terms that are common throughout the whole polynomial. If so, divide it out. Then see if you can simplify it more, for example using the quadratic formula if the biggest power is 2.

6x^3+18x^2:
-To factor, first see which terms are common to each part of the equation and factor them out.
-Notice that you can simplify this equation first by factoring out the 6 and the x^2, which are common to both terms. You get:
6x^2(x +3)

3m^2+24m+36
-The only thing common to all parts of this equation is the 3. Factor it out first: