Please show how to factor this 3x^2 -10x-8.

Step-by-step explanation:

Something to keep in mind is that the factored expression will be in either the form of or . 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

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, 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

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

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

(Sorry that this explanation was quite lengthy)

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