Factoring Help

Hey guys. I had about two hundred of these to do, but I could get a few. If anyone can work a few or all of these out, I would GREATLY appreciate it!

When I put 4x^2, I mean four x squared.

4x^2-13x-27
3x^2+54x+243
112x^2-168x+63

Factor into simplest terms please!

Wait... (4x)^2? Or 4(x)^2?

Okay... I'm doing these anyway.

4x^2-13x-27

4 * -27 = -108=0

Now, what can divide in -108 that, when added, can equal -108?

12*9=108
4*27=108
18*6=108

Okay, what about -108?

-18*6=108
6-18=-13

So!

4x^2+6x-18x-27 =0
2x(2x+3)-9(2x-3)=0
(2x+3)(2x-9)

2x+3=0
2x=-3
x=-3/2

2x-9=0
2x=9
x=9/2

So, two answers

x=-3/2
x=9/2

Help any?

They look to me to already be in simplest terms...What exactly are we working with? Are these polynomials?

Well... simplest terms may be: (2x+3)(2x-9)

Something like that.

OH! I am so dumb! Now I remember...

Okay... This may sound weird, but I love factoing, so:

3x^2+54x+243
is divisible by 3, so:
3(x^2+18x+81)

which turns into (x+9)(x+9)


*****


112x^2-168x+63

is equal to

7(16x^2-24x+9)

which will eventually turn into (4x-3)(4x-3)

My brain hurts