Question 12560: I am trying to learn about the quadratic equations. I know how to turn (3x-4)(2x+1)=0, but I don't know how to turn 6x^2 -5x -4=0 into (3x-4)(2x+1)=0.
-Sarah
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Well, going from: to  is a whole lot easier than going the other way.
Here are some things you might try on factoring  for example:
1) Look at the first term  and ask...how can I factor ?
There aren't that many ways to factor it.
Now look at the last term  and go through the same process.
 This is really the same as the one above.
Now, keeping in mind that you want -5x as the middle term, you can try a pair of factors from the first group with a pair of factors from the second group.
For example: Try (6x - 1)(x + 4) and you see, almost right away that, while you get the first and last terms of your quadratic, you do not get -5x as the middle term. The same with (6x + 1)(x - 4) and (6x + 4)(x - 1).
Now try (3x + 1)(2x - 4) again, you don't get the middle term of -5x, so try (3x - 4)(2x + 1) Now you get a middle term of -5x from 3x - 8x = -5x.
So, these are the required factors.
It's a little harder when, as in this case, the coefficient of the x^2 term is greater than 1. Indeed, in some cases, you may not be able to factor the quadratic at all. But, you can always solve a quadratic equation by using the quadratic formula: 
I hope this is some help. I have one math book on Intermediate Algebra that devotes some 36 pages to the topic of factoring polynomials.
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