Question #d5777

2 Answers
Dec 5, 2017

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

Dec 5, 2017

(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).