Question

How do you factor the trinomial `x^2-4x-12`?

Answer 1

`f(x) = (x-6)(x+2)`

Explanation:

`f(x)=ax^2+bx+c`

All you have to do is find two numbers which added give you `b` and multiplied give you `c`.

Those numbers are `-6` and `2`.

`f(x) = (x-6)(x+2)`

`f(x) = x^2+2x-6x-12`

`f(x) = x^2-4x-12`

Answer 2

`(x-6)(x+2)`

Have a look at the explanation

Explanation:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The trick is to spot what value for a and b give you

`ab=12` We need -12 so one of a and b is negative and the other positive

`a-b =4` We need -4 so the larger of a and b is negative

Consider the factors of 12

`color(red)(1 times 12" and the difference is 11 so it fails")`

`color(green)(2 times 6 " and the difference is 4 so it works")`

`color(red)(3 times 4" and the difference is 1 so it fails")`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Try 1
`(x + 6)(x - 2)` The larger being positive which is the wrong way
`color(white)(xxxxxxxxxx)`round to what we stated

`= x^2 -2x +6x -12` This fails as it gives `+4x`

Try2
`(x-6)(x+2)`

`=x^2 +2x-6x-12`

`= x^2-4x-12` This works so it is the answer!