Question

Question #d5777

Answer 1

`x=-2,3`

Explanation:

Start off by organizing `-4x+24-4x^2` properly. Like this:
`-4x^2-4x+24`

I'd start off by doing the Slip and Slide method that was taught at my school. So, I'd multiply `-4` (from the `x^2`) and `24` together.

`-4x^2-4x+24`
to
`x^2-4x-96`

Notice how I put the product of `-4 * 24` into the last space of the equation. (the `-4` will come into play soon, so don't forget about it just yet!)

Now factor the equation! Two numbers that equal `-96` when multiplied and `-4` when added together are `8` and `-12`.

The equation for this would be from `x^2-4x-96` to this:

`(x+8)(x-12)`

Next, divide `8` and `-12` by `-4` (the one that we took out earlier and multiplied with `24`). The remaining answer should look like this:

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

Therefore, `x=-2,3`

Answer 2

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

Explanation:

It is always easier to start by rewriting the expression in standard form.

`- 4x +24-4x^2`

`-4x^2-4x+24`

Now to find the factors, we must factor. The first step is to set the expression equal to `0` to make it an equation.

`-4x^2-4x+24=0`

It is easier if the coefficient of `x^2` is not a pesky negative. We can simplify by dividing both sides of the equation by `-4`.

`x^2+x-6=0`

From here we use the technique where we must find `2` numbers that equal `c` in the expression `ax^2+bx+c` that will also add up to equal to `b`.

Two numbers that satisfy this are `-2` and `3`.

We can check:

`(-2)(3) = -6`
`(-2) + (3) = 1`

Now we just break up `x^2+x-6` using the numbers we just found.

`(x-2)(x+3)=0`

So the factors of `- 4x +24-4x^2` are `(x-2)` and `(x+3)`.