Factor completely 6x^2+13x-8

To factor the expression 6x^2+13x-8 completely, we can look for two binomials that multiply together to give the original expression.

First, we will look for two numbers that multiply together to give -48 (the product of 6 and -8), and add together to give 13 (the coefficient of the middle term).

The numbers that satisfy these conditions are 16 and 3.

So, we can rewrite the expression as:

6x^2 + 16x - 3x - 8

Next, we can factor by grouping.

Taking out the common factor from the first two terms, we get:

2x(3x + 8) - 3x - 8

Taking out the common factor from the last two terms, we get:

2x(3x + 8) - 1(3x + 8)

Now, we can see that both terms have a common factor of (3x + 8).

Therefore, the factored form of 6x^2 + 13x - 8 is:

(3x + 8)(2x - 1)