We can use our set of Algebra Tiles to illustrate adding polynomials. Click HERE if you need to print and cut out a set of your own Algebra Tiles. Let us show you each tile and what it stands for: This tile is the positive one tile. This is your negative one tile.
If you place the two
tiles beside each other, you create a ZERO. This tile stands for a single x. It is one unit wide and an unknown or "x" number of units long. *NOTE: an even number of "one unit" () tiles will NOT fit on this tile. It is supposed to be a "mystery" size. This represents the opposite of x, or negative one x. Placing these two together also creates a ZERO. x + (-x) = 0 Here we have the positive one x squared tile. It measures "x" on both its length and width (both are "mystery" lengths i.e. not multiples of the one unit square). Therefore its area is x^2. And here we have the opposite of the x square tile, or negative one x squared. As above, when placed together these tiles create a big, fat, ZERO. x^2 + -x^2 = 0. Now let's start making some polynomials with our tiles, and we will add them as we go. To create the binomial 3x^2 + (-2x).....more commonly written as 3x^2-2x, lay these tiles out on our desk.
Now let's add to this the trinomial -5x^2 + 3x +(-2).
Now make all the ZERO'S that you can and pull them off your desk. The tiles that remain will be the answer to the addition problem.
the answer is -2x^2 + x + (-2) Practice a few with your own tiles. Click the answer links to see if you are correct.
Have fun TOUCHING your Algebra!
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