Factor polynomial $$ x^{2}-x-132 $$

$$ x^{2}-x-132 = ( x+11 )( x-12 ) $$

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:

$$ \color{blue}{ b = -1 } ~ \text{ and } ~ \color{red}{ c = -132 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ -1 } $ and multiply to $ \color{red}{ -132 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = -132 }$.

PRODUCT = -132
-1     132	1     -132
-2     66	2     -66
-3     44	3     -44
-4     33	4     -33
-6     22	6     -22
-11     12	11     -12

Step 3: Find out which pair sums up to $\color{blue}{ b = -1 }$

PRODUCT = -132 and SUM = -1
-1     132	1     -132
-2     66	2     -66
-3     44	3     -44
-4     33	4     -33
-6     22	6     -22
-11     12	11     -12

Step 4: Put 11 and -12 into placeholders to get factored form.

$$ \begin{aligned} x^{2}-x-132 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}-x-132 & = (x + 11)(x -12) \end{aligned} $$

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