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:
 Write the 1^{st} term in cell 1.
 Write the 3^{rd} term in cell 2.
 Write in cell 3 the product of the numbers in cells 1 and 2.
 In cells 6 and 9, write new terms whose product equals the number in cell 3 but whose sum equals the 2^{nd} term of the trinomial.
 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.
 In cell 5, write the quotient of the numbers in cells 6 and 4.
 In cell 8, write the quotient of the numbers in cells 9 and 7.
 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)
