A. Factoring using Tiles
- A = l • w (l and w are factors of A)
- A = x2 ® "x2" tiles
- A = x ® "x" tile
- A = 1 ® "#" tile
** Blue, Green, and Yellow are the positive sides.
** Red is the negative side.
- Represent the trinomial with correct color and number of tiles.
- Construct a large rectangle using these pieces.
- "x2" tile(s) go in the upper left corner.
- "x" tiles go to the right and bottom of the "x2" tile(s).
- "#" tiles go in the bottom right corner.
- If there are too many "#" tiles, then add a zero - one at a time - which is a positive and negative "x" tile.
- Put the positive "x" tiles together and the negative "x" tiles together.
Determine the length of the edge across the top and down the left side of the rectangle – these are the two binomial factors.
Check factors mentally with F-O-I-L.
B. Factoring using the 6-Step Method ax2 ± bx ± c
- Multiply "a" and "c".
- Find two factors of this product that add to equal "b."
Use these two factors to rewrite the linear term as two terms when writing out the problem again.
- When a = 1 stop here. The two numbers chosen will be the numbers in the two binomial factors.
Group the first two terms together and the last two terms together.
- When you have a choice, write the negative term first.
Factor the GCF out of each set of parentheses.
- If the third term from the left has subtraction in front, add the opposite before grouping.
Determine the two binomial factors.
- If you added the opposite in step 4, factor a negative GCF out of the second set of parentheses.
- One factor will be the common set of parentheses.
- One factor will be the two GCFs put together.
C. Using the Discriminant to Determine if Factoring Can be Done
- Evaluate the discriminant: b2 - 4ac.
- If the value can be square rooted evenly, the expression CAN be factored.
- If the value cannot be square rooted evenly, the expression CANNOT be factored.
D. Factoring Completely
- Difference of Two Squares
- Perfect Square Trinomial
- 6-Step Method with the Short-Cut
- 6-Step Method