Question #d5777

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Question #d5777

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Answer 1 · 2017-12-05T00:30:49

$x = - 2, 3$ $x=-2,3$

Explanation:

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

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

$- 4 x^{2} - 4 x + 24$ $-4x^2-4x+24$
to
$x^{2} - 4 x - 96$ $x^2-4x-96$

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

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

The equation for this would be from $x^{2} - 4 x - 96$ $x^2-4x-96$ to this:

$(x + 8) (x - 12)$ $(x+8)(x-12)$

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

$(x + 2) (x - 3)$ $(x+2)(x-3)$

Therefore, $x = - 2, 3$ $x=-2,3$

Answer 2 · 2017-12-05T01:50:09

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

Explanation:

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

$- 4 x + 24 - 4 x^{2}$ $- 4x +24-4x^2$

$- 4 x^{2} - 4 x + 24$ $-4x^2-4x+24$

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

$- 4 x^{2} - 4 x + 24 = 0$ $-4x^2-4x+24=0$

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

$x^{2} + x - 6 = 0$ $x^2+x-6=0$

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

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

We can check:

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

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

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

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

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Question #d5777

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