When you factor a number, you are writing the number as a product of two numbers. Usually (not always), the two numbers are smaller than the original and different from each other. For example, one way to factor 6 is to write it as 3*2 which says "3 times 2". Another example is to take a number like 32 and write it as 8*4.

The x is simply a placeholder for a number, so we can apply the same factoring rules to algebra as you've done in the past with regular numbers. Something like 9x is really a factorization of its own because it means 9 times x where x is some unknown number. If x were say x = 2, then 9x = 9*2 = 18.

We can rewrite 9x into 3*3x because 9 is the same as 3*3. The +3 at the end of 9x+3 can be turned into 3*1.

So we go from this: 9x+3

To this: 3*3x+3*1

At this point, it might seem like we're just complicating something just for the fun of it. In reality, we're helping ourselves to factor out a common term of 3. Use the distribution rule to go from 3*3x+3*1 to 3*(3x+1). If you were to distribute the outer 3 back into each term, then you'd get 3*3x+3*1 = 9x+3 again. So in a way, you can think of it as distribution but in reverse. Factoring pulls things apart while distribution puts it back together. That's possibly one way to remember it.

So in the end, 9x+3 completely factors to 3*(3x+1). Note how we have a product of two expressions 3 and 3x+1

This might seem like a lot of steps but it's not that bad. Once you have enough practice, you'll be able to do this in one or two steps fairly easily. I'll let you practice the others on your own. They are similar to problem 1. If you still are stuck, then let me know and I'll update the solution.