Arranging powers of x in columns

If you have a lot of algebra to crunch and you have powers of x on both sides of the equation, instead of moving them one term at a time, lay them out like a subtraction with the left hand side above and the right hand side below.

Note: this will only work if the only things you have are powers of x. If you have sin or cos or other functions as well, or another variable like y, don't do it.

For example, if you have 4x² - 3x + 2 = -2x² + 4x + 12

instead of subtracting terms one at a time to move them from the right to the left, line the whole thing up like a subtraction sum. Leave clear spaces for the x² column, the x column and the constant column. Write it as

	4x2	- 3x	+ 2
-[	-2x2	+4x	+12	] = 0

If you line them up properly then you can do it like a subtraction sum in arithmetic, to get

6x² - 7x -10 = 0

You still have to be careful with negative numbers, of course.

If you get really confident about this, you can actually omit writing the x² etc and just put them at the head of each column. This becomes like using positional notation in normal decimal numbers.

	x2	x	1		4	- 3	+ 2
-[	-2	+4	+12	] = 0

Experiment this way, but make sure that you are confident that you know what you are doing.