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Algebra I Recipe: Factoring Quadratic Trinomials ax² ± bx ± c into Two Binomials
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.


  1. Represent the trinomial with correct color and number of tiles.
  2. 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.


  3. Determine the length of the edge across the top and down the left side of the rectangle – these are the two binomial factors.
  4. Check factors mentally with F-O-I-L.
ExamplesExamples:
x2 - 5x + 6

x2 + 2x – 8

2x2 + 6x – 8

2x2 - x – 6

B. Factoring using the 6-Step Method ax2 ± bx ± c
  1. Multiply "a" and "c".
  2. Find two factors of this product that add to equal "b."
    • When a = 1 stop here. The two numbers chosen will be the numbers in the two binomial factors.
  3. Use these two factors to rewrite the linear term as two terms when writing out the problem again.
    • When you have a choice, write the negative term first.
  4. Group the first two terms together and the last two terms together.
    • If the third term from the left has subtraction in front, add the opposite before grouping.
  5. Factor the GCF out of each set of parentheses.
    • If you added the opposite in step 4, factor a negative GCF out of the second set of parentheses.
  6. Determine the two binomial factors.
    • One factor will be the common set of parentheses.
    • One factor will be the two GCFs put together.
ExamplesExamples:
2x2 - 7x – 4

x2 + 6x – 16

2x2 + 7x + 5

6x2 - 13x + 5

C. Using the Discriminant to Determine if Factoring Can be Done
  1. Evaluate the discriminant: b2 - 4ac.
  2. If the value can be square rooted evenly, the expression CAN be factored.
  3. If the value cannot be square rooted evenly, the expression CANNOT be factored.
ExamplesExamples:
2x2 + 3x – 6

6x2 + 5x – 4

D. Factoring Completely
  1. GCF
  2. Difference of Two Squares
  3. Perfect Square Trinomial
  4. 6-Step Method with the Short-Cut
  5. 6-Step Method
  6. Grouping
ExamplesExamples:
3x3 - 48x

32x3 - 16x2 + 2x

32x5 - 2x




G Redden

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