Saturday, December 26, 2009

Simple Trick for Factoring any Trinomial ax^2 + bx + c = 0

Most students find it  easy to factor trinomials when the leading coefficient is 1, but a whole other story when the leading coefficient is another number. I learned this trick at a math conference I went to in Oklahoma City a couple of years ago. By following the steps mentioned, it is easy to change any trinomial into a trinomial that has 1 as it's leading coefficient, making the rest of the process fairly easy for most students.

How to factor any trinomial as a trinomial with a leading coefficient of 1.

1) Multiply a * c to get the new "c" value and give "a", a value of 1. i.e. 2x^2 + 7x + 6 = 0. Multiply 2 * 6 = 12. Put in 12 for "c" and 1 for "a".
                       Your new trinomial is; x^2 + 7x + 12 = 0

2) Factor with leading coefficient having a value of 1 and solve for x. (factors for c that add up to equal b)
                              i.e. (x + 3) (x + 4) = 0, x = { -3, -4}

3) Divide solutions by the original leading coefficient ( In this example the original value for "a" was 2). You’re done!
                               i.e.   x = {-3/2, -2} (2x +3) (x + 2)

1 comment:

  1. My math teacher in high school taught me this trick. I found it very useful until I forgot it. I am now in Calculus in college, and I really wanted to remember this trick! Thanks for posting this on your blog; I am now able to factor problems much faster on my calc exam!