Factor 6x^2-13x-5?

Question

Factor 6x^2-13x-5?

Answer 1

There is a way to do this without just trying various possibilities...

Look at the coefficient of the largest exponent term which is the 6 from 6x²

Multiply that coefficient by the constant at the end of the expression... 6(-5) = -30

What you want are to find factors of -30 that add to the middle coefficient... in this case -13

The factors of -30 that add to -13 are (-15)(2)

Thus swap your -13x out for -15x + 2x then group and factor the resulting equation

 

We have two possibilities ...   6x^2-13x-5 =  6x² -15x + 2x -5   or    6x² + 2x -15x -5

We look at the first two terms and last two terms to see which sets are easily factorable..

In this case I see that in the 2nd equation I can easily factor 2x from the 1st two terms and -5 from last two

 

So group the equation as..  6x² + 2x - 15x - 5

                                       = 2x(3x + 1) -5(3x + 1)

                                       = (2x -5)(3x + 1)

Answer 2

You just have to play with it a little bit.

The "6x^2" can be 6x * x, or it can be 3x * 2x.  The "-5" on the end can only be 5 * -1 or -5 * 1.

I am going to try this:

 

(3x + 1) (2x - 5)

To check my work, I will FOIL it out.

 

3x * 2x is 6x^2
3x * -5 is -15x
2x * 1 is 2x
-15x + 2x is -13x so that checks.
And, 1 * -5 is -5.

So, it's good.

The trick is to find the factors of the lead coefficient (the 6) and of the constant term (the -5), and then play with them until you get the desired results.