Factor polynomial $$ x^{2}+8x-33 $$

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

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:

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

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.

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

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