Answer:
(3x - 4)(2x - 1)
Explanation:
6x^2 - 5x - 4
When factoring, we want to first find the GCF. In this case, the GCF is one so we leave it as that. Next, we want to try and find the sum and the product. Additionally, we have a leading coefficient. We will multiply the leading coefficient by the last term, which is -4. (You will need to remember this to continue on later.)
x^2 - 5x - 24
Now, we can find the sum and the product. To do this, we need to list the factors of 24. (Remember negatives as well!)
24: 1 and 24, 2 and 12, 3 and 8, 4 and 6.
As -24 is also a negative, that means it will have one positive and one negative factor. This must also add up to -5.
One pair that does this is -8 and 3. They multiply together to -24 and add up to -5.
Now, since we multiplied the leading coefficient in the beginning, we must bring it back down into the parenthesis.
(6x - 8)(6x - 3)
We must divide out and try to simplify this as much as we can to match the leading coefficient. The divisors must multiply up to 6.
(6x - 8)/2 and (6x - 3)/3. 3*2 = 6
(3x - 4)(2x - 1)