2. When you see perfect squares like 9 and 16 the first thing to think of is the square roots and see how those work. (3x+4)(3x+4)
3. The second thing to think of when there is a number (coefficient) in front of the x^2 is to see if that can be factored out of each term. In this case 12 will factor into 36 but not 46 so look at the factors of 12 to see if we can take out a smaller number. How about factoring out a 4? 4 won't go into 46 evenly so lets try a 2. 2(6x^2 + 23x - 18) Now can we factor what's in the ( )? let's try 2 and 3 for the 6
(2x + ?)(3x - ?) Notice that because the last term is a negative then our factors will have to be one a + and one a -. So lets try (2x + 3)(3x - 6) That doesn't work because you end up with a middle term of -12. Lets try 2 and 9 (2x+ 2)(3x -9) That gives us -12 so that doesn't work either. Lets switch them around and try (2x + 9)(3x - 2). That gives us +27 and - 4. That's what we need! So the final answer would be 2(2x + 9)(3x - 2)
4. When you are dividing like base numbers you subtract the exponents 5^6 divided by 5^4 = 5^(6-4) = 5^2.