Answer:
When factoring, you want to get all of the terms on one side first and set all of it equal to 0. Many of the problems here are already in this format =0, but there are some where you'll have to move the terms around.
In these examples, it also looks like the highest power you have is x^2. This makes things easier to work with.
Let's just start with the first one, x^2 - 9x + 18 = 0.
We need to find two numbers that multiply to give us 18, and add together to give us -9. That would be -6 and -3.
-6 + -3 = -9
- 6 * -3 = 18
We can rewrite it now. This is the factored form.
(x - 6) * (x - 3) = 0
If you want to, you can go back to expanded form using the acronym 'FOIL'. First, Outside, Inside, Last. This refers to the order of multiplying the terms.
(x - 6) * (x - 3)
x * x = x^2
x * -3 = -3x
-6 * x = -6x
-6 * -3 = 18
Simplify
x^2 - 3x - 6x + 18 = 0
And we're back to where we started.
x^2 - 9x + 18 = 0
Hope this helps.