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Nine Celled Square Method
A couple of years ago, I learned an easy way to factor polynomials. It is much easier than other methods such as trial and error. It is called the Nine Celled Square Method. I have looked everywhere on the internet, and I cannot find it. Luckily, I found an old handout from my former algebra teacher. I have copied the information into a word document which I have included with this message. I hope this helps a lot of students looking for the same information I was!

Jeff Schmidt
jbschmidt@mail.com
Example: Factor 2x^2 +11x + 15

Steps:
  1. Write the 1st term in cell 1.


  2. Write the 3rd term in cell 2.


  3. Write in cell 3 the product of the numbers in cells 1 and 2.


  4. In cells 6 and 9, write new terms whose product equals the number in cell 3 but whose sum equals the 2nd term of the trinomial.


  5. In cells 4 and 7, write new terms whose product equals the number in cell 1. Number in cell 4 must be divisible into the number in cell 6, and the number in cell 7 must be divisible into the number in cell 9.


  6. In cell 5, write the quotient of the numbers in cells 6 and 4.


  7. In cell 8, write the quotient of the numbers in cells 9 and 7.


  8. Your answer will be the product of the two sums: the sum of cells 4 and 8, and the sum of cells 5 and 7.

1.

2x^2

2.

15

3.

30x^2

4.

1x

5.

5

6.

5x

7.

2x

8.

3

9.

6x



Answer = (x + 3)(2x + 5)

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