Factor polynomial $$ w^{2}-8w-33 $$

$$ w^{2}-8w-33 = ( w+3 )( w-11 ) $$

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:

$$ \color{blue}{ b = -8 } ~ \text{ and } ~ \color{red}{ c = -33 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ -8 } $ and multiply to $ \color{red}{ -33 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = -33 }$.

PRODUCT = -33
-1     33	1     -33
-3     11	3     -11

Step 3: Find out which pair sums up to $\color{blue}{ b = -8 }$

PRODUCT = -33 and SUM = -8
-1     33	1     -33
-3     11	3     -11

Step 4: Put 3 and -11 into placeholders to get factored form.

$$ \begin{aligned} w^{2}-8w-33 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ w^{2}-8w-33 & = (x + 3)(x -11) \end{aligned} $$

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