Factor polynomial $$ -x^{2}-x+56 $$

$$ -x^{2}-x+56 = -( x-7 )( x+8 ) $$

Step 1 :

After factoring out $ -1 $ we have:

$$ -x^{2}-x+56 = - ~ ( x^{2}+x-56 ) $$

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:

$$ \color{blue}{ b = 1 } ~ \text{ and } ~ \color{red}{ c = -56 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ 1 } $ and multiply to $ \color{red}{ -56 } $.

Step 3: Find out pairs of numbers with a product of $\color{red}{ c = -56 }$.

PRODUCT = -56
-1     56	1     -56
-2     28	2     -28
-4     14	4     -14
-7     8	7     -8

Step 4: Find out which pair sums up to $\color{blue}{ b = 1 }$

PRODUCT = -56 and SUM = 1
-1     56	1     -56
-2     28	2     -28
-4     14	4     -14
-7     8	7     -8

Step 5: Put -7 and 8 into placeholders to get factored form.

$$ \begin{aligned} x^{2}+x-56 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}+x-56 & = (x -7)(x + 8) \end{aligned} $$

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