3x+4
+  x-6
--------
3x^2-2 

No you wouldn't get any x^2 unless you were multiplying.       
You're adding not multiplying. When you add pencils to
pencils you get pencils, not "pencils squared"! So when
you add x's to x's you get x's, not x^2's Here's howa;

First write a + in front of the 3x and a +1 in front of
of the x on the bottom:

  +3x+4
+ +1x-6
--------

Now add the +3x and +1x.  That's just +4x. (You don't get
any x^2, just x.) So write that below the line

  +3x+4
+ +1x-6
--------
  +4x

Then you add +4 and -6.  They have different signs so
you find the difference of 2, and then make it -2 because
6 is larger than 4:

  +3x+4
+ +1x-6
--------
  +4x-2

That's the answer. You can erase the + in front and the
answer is:

   4x-2
----------------------------
---------------------------
  
  2x-1
+ -x+1
--------
2x^2-0 < again my wrong answer

Again you got x^2 and you multiplied when you should have
added.  Here's how to do that.

First write a + in front of the 2x and a -1 in front of the 
x on the bottom:

  +2x-1
+ -1x+1
--------

Now add +2x and -1x.  They have different signs so
you find the difference of 1x, and then make it +1x
because 2x is larger than 1x:


  +2x-1
+ -1x+1
--------
  +1x 

Now you add -1 and +1, and get +0, so you have this:

  +2x-1
+ -1x+1
--------
  +1x+0

But you don't have to write the 0 and the answer
is just +1x, but then you drop the + and the 1 and the
answer is just x.

Edwin