[denamontgomery]

I am trying to factor a quadratic equation

[Unknown008]

Ok, I'll give and example:

1. Break down the factors of the term without 'x' and the one with x^2

-2: 1 x - 2 or 2 x -1
3: 1x x 3x

2. Put one set of factors from the first one (-2) with the other set of factors (3) as follows[the factors are put vertically]:

1ooo1xooio| 1x
-2ooo3xooo| -6x
oooooooooo-5x

Now, multiply the horizontal numbers. 1 x 1x = 1x, -2 x 3x = -6x.
Then, add both. 1x + (-6x) = -5x

Now, -5 is not what you're looking for since the term in 'x' in your original equation is +5.

Try with other factors:

-1ooo1xooo| -1x
2ooo3xooio| 6x
oooooooooo5x

Now, you have +5x, which is the good one.

Then, group the diagonal factors in brackets, adding them and putting both groups side by side, don't forget the equal sign and the zero!

(-1+3x)(2+1x) = 0

If you expand this, you should have the original equation back.

Putting the above equation 'cleaner' gives: (3x-1)(x+2)=0

You know that any number multiplied by zero gives zero? Well, that means that either (3x-1) = 0, or (x+2) = 0.

3x-1 = 0

Solve for x to obtain the first answer.

x+2 = 0

Solve for x to obtain the second factor.

The answers for x are 1/3 and -2.

I hope it helped! :)

EDIT: Anyway, that's how I learned it the first time.

[ebaines]

For a general description of factoring, see:

Factorization - Wikipedia, the free encyclopedia