Answer:
[tex](3x+2)(x-4)[/tex]
Step-by-step explanation:
Something to keep in mind is that the factored expression will be in either the form of [tex](ax-b)(x-c)[/tex] or [tex](ax-b)(cx-d)[/tex]. In either case, the final term will only be the product of -b and -c in the first case or -b and -d in the second case. This means that the term without an x will not be affected by the coefficient of x.
We have the following expression
[tex]3x^2-10x-8[/tex]
The first thing we can do is list out the factors of -8
1 and -8
-1 and 8
2 and -4
-2 and 4
These are all of the pairs that could be factors of -8.
Normally, the next step would be to look for which of these factors would add together to give you the coefficient of x, but as there is a 3[tex]x^2[/tex], this is complicated a little more.
Instead, we have to look for 3 multiplied by one of the factors and then added to the other factor. In the case of this problem, the result must be -10.
At this point, you just have to begin testing out which ones will work.
Let us look at the factors 2 and -4
[tex]2(3)-4=2\\\\2-4(3)=-10[/tex]
We can see that while the first one didn't work, the second one resulted in -10, which is what we wanted.
Now that we know what the factors are, let us write them in the form[tex](ax-b)(x-c)[/tex]
Normally, it does matter which number you pair with each x, but in this case, it does matter. As we had to multiply the -4 by 3, it must be in the pair that is opposite to the pair with the 3x.
Knowing this, we can construct out factor
[tex](3x+2)(x-4)[/tex]
(Sorry that this explanation was quite lengthy)
