Question

How do I factor 6x^2-x-8

Answer 1

You can do by guessing or by grouping.

Answer 2

In this case, by guessing is not too bad, since 6 can only be factored as 6 * 1 and 2 * 3.

Answer 3

I would start with a guess of 6 = 2 * 3.
That means
6x^2 - x - 8 = (2x )(3x )

To finish this, now we need two numbers that multiply to -8.
-8, 1
-1, 8
-2, 4
-4, 2

Answer 4

Now we need to find which two factors of -8 and in which position will gives the correct factoring.

Answer 5

Let's try -2, 4:

6x^2 - x - 8 =? (2x - 2)(3x + 4)
To check, we do the OI steps of FOIL to see if the middle term is the correct one.

OI: 2x * 4 + (-2)(3x) = 8x - 6x = 2x. Doesn't work bec we need -x

Answer 6

Let's try 4, -2:

6x^2 - x - 8 =? (2x + 4)(3x - 2)
To check, we do the OI steps of FOIL to see if the middle term is the correct one.

OI: 2x * (-2) + (4)(3x) = -4x + 12x = 8x. Doesn't work bec we need -x

Answer 7

You can keep trying the other combinations of factors of -8 to see if any of them works.

Answer 8

Before you do that, though, try using the discriminant of the quadratic formula.
If the square root of the discriminant is rational, then you can factor the trinomial. If it is not rational, then it can't be factored.

Answer 9

Thank you so much!

Answer 10

wlcm