This instructable will show you how to use an Epilog laser cutter to make a set of the useful tiles. If you do not have a laser cutter, you can use Ponoko or similar laser cutting services to make yours.
Step 1: Supplies
Sheets of Acrylic (32 dollars for a 24x34 inch piece from Tap Plastics)
A Laser Cutter
The template that is attached
I included 2 templates, one for 1 set and one for a set of 39. They can be edited in corel draw or a similar program.
Step 2: Laser Cut The Acrylic
Engraving: 400 dpi Speed: 100 Power: 40
Cutting: 400 dpi Speed: 10 Power: 100 Frequency: 5000
I removed the paper off the acrylic as to help the engraving, with the paper on you'll have to change your settings.
Step 3: Finished Tiles
Once you laser cut them, use a toothpick to poke out the extra plastic. Then you are left with the pretty tiles.
Step 4: How To Use The Tiles
x2 Tile which has side x
x Tile which as an x and a 1 side
and the 1 Tile that has a 1x1 sides
Each tile has a positive side (denoted by the lines) and a negative side (smooth side)
In our picture example we see the trinomial:
x2 + 2x + 1
When the tiles are fitted together we see it makes a perfect square, and looking at each side we can see that each side makes up x+1
Therefore the prime factor of the trinomial is (x+1)2