Factor polynomial $$ 8x^{2}-16x-192 $$

$$ 8x^{2}-16x-192 = 8( x+4 )( x-6 ) $$

Step 1 :

After factoring out $ 8 $ we have:

$$ 8x^{2}-16x-192 = 8 ( x^{2}-2x-24 ) $$

Step 2 :

Step 2: Identify constants $ \color{blue}{ b }$ and $\color{red}{ c }$. ( $ \color{blue}{ b }$ is a number in front of the $ x $ term and $ \color{red}{ c } $ is a constant). In our case:

$$ \color{blue}{ b = -2 } ~ \text{ and } ~ \color{red}{ c = -24 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ -2 } $ and multiply to $ \color{red}{ -24 } $.

Step 3: Find out pairs of numbers with a product of $\color{red}{ c = -24 }$.

PRODUCT = -24
-1     24	1     -24
-2     12	2     -12
-3     8	3     -8
-4     6	4     -6

Step 4: Find out which pair sums up to $\color{blue}{ b = -2 }$

PRODUCT = -24 and SUM = -2
-1     24	1     -24
-2     12	2     -12
-3     8	3     -8
-4     6	4     -6

Step 5: Put 4 and -6 into placeholders to get factored form.

$$ \begin{aligned} x^{2}-2x-24 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}-2x-24 & = (x + 4)(x -6) \end{aligned} $$

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