Factor polynomial $$ x^{2}-5x-66 $$

$$ x^{2}-5x-66 = ( x+6 )( x-11 ) $$

Step 1: 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:

$$ \color{blue}{ b = -5 } ~ \text{ and } ~ \color{red}{ c = -66 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ -5 } $ and multiply to $ \color{red}{ -66 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = -66 }$.

PRODUCT = -66
-1     66	1     -66
-2     33	2     -33
-3     22	3     -22
-6     11	6     -11

Step 3: Find out which pair sums up to $\color{blue}{ b = -5 }$

PRODUCT = -66 and SUM = -5
-1     66	1     -66
-2     33	2     -33
-3     22	3     -22
-6     11	6     -11

Step 4: Put 6 and -11 into placeholders to get factored form.

$$ \begin{aligned} x^{2}-5x-66 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}-5x-66 & = (x + 6)(x -11) \end{aligned} $$

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