Question

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

Answer 1

(x-4)(3x+2)

Explanation:

Answer 2

`(3x+2)(x-4)`

Explanation:

Something to keep in mind is that the factored expression will be in either the form of
`(ax-b)(x-c)` or
`(ax-b)(cx-d)`. 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

`3x^2-10x-8`

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
`x^2`, 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

`2(3)-4=2\\\\2-4(3)=-10`

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
`(ax-b)(x-c)`

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

`(3x+2)(x-4)`

(Sorry that this explanation was quite lengthy)