Question

How do you factor `3x^2-4x-4`?

Answer 1

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

Explanation:

Let's start by putting empty brackets.

`( ) ( )`

We know that `3x^2` is `3x xx x`.
We can place each of these into one of the brackets.

`(3x )(x )`

Then we look at the factors of -4. What are all the ways we can multiply two numbers to get -4?

`1xx-4=-4`
`2xx-2=-4`

Now the tricky part is figuring out which pair we need to use, and where to put each. With practice this will get easier, but at first you might have to try each of them one by one. I'll start with the correct pair, that is +2 and -2.

`(3x+2)(x-2)`
To check whether this is correct we can expand it again. Remember you have to multiply each value in the second bracket by each of the values in the first.

So
`3x xx x=3x^2`
`3x xx-2=-6x`.
Then
`2 xx x=2x`
`2 xx -2=-4`.

All of these together gives us `3x^2 -6x +2x -4` which is `3x^2-4x-4`. Ta-da!

If we had reversed the factors by putting `(3x-2)(x+2)`, it would have given us `3x^2+4x-4`, which is close but not exactly what we are looking for.

If we had used the other pair of factors, that is 1 and -4, we'd have gotten `(3x+1)(x-4)` which would be `3x^2-11x-4`
or `(3x-4)(x+1)` which would be `3x^2-x-4`.