Week 8 – Math 10

This week we’ve started our Polynomial unit. This was more of a review/recap of polynomials in grade 9 (algebra tiles) but now instead of an equation with 3 units (ex. 2(x + 1) ) We are using 4 units (ex. (2x + 1)(x + 3) ). We also discussed how to solve these polynomial equations algebraically.

This is the equation we will be using.

First off is knowing what the algebra tiles are. Algebra tiles are mathematical manipulatives, which helps students understand algebraic equations easier. In this image I am showing what each tile means and what its “worth” is. Coloured tiles are positive and the white/uncoloured tiles are negative.

Now you draw this chart where the tiles will be placed.

You place one of the equations in the brackets on either the top or bottom. In this case I put (x + 3) from the equation (x + 3)(x – 2) on the top and (x + 2) on the side.

Now i drew lines straight across creating our tiles in the center of the diagram.

I coloured in the area and labeled its “worth”. To know if the tile in the area will be positive or negative depends on the tiles on the outside. A +Tile and a +tile from the outside = a +tile(same tiles (++ or — = +) equals a positive tile). And if the tiles are different (- +) it will be a -Tile.

Since now I have my tiles coloured and that I know which are positive and negative I can cross out my zero pairs (a pair of numbers whose sum is zero ;ex. +1, -1). Now I am left with only 1x.

Finally to write out the equation. You take what tiles are left and write it out creating your answer.

Now to do the same but this time algebraically. We start off with the same equation.

Firstly you split up the equation so you know how to solve it (I coloured it to make the visual easier to figure out)

Since it is now split up, you now need to disperse the outside # into the numbers inside the bracket.

Once doing that you should end up with a equation like so with 2 numbers with the same symbol(x)

Since these 2 numbers have the same symbol you are able to add them together. (for adding and subtracting you can only Add/sub if the symbol is the same (x & x). If the symbols are different they cannot be added/Sub.)

(-2x +3x = 1x.) This should be the final product.

(Whole photo)