Factor polynomial $$ x^{2}+x-272 $$

$$ x^{2}+x-272 = ( x-16 )( x+17 ) $$

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:

$$ \color{blue}{ b = 1 } ~ \text{ and } ~ \color{red}{ c = -272 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ 1 } $ and multiply to $ \color{red}{ -272 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = -272 }$.

PRODUCT = -272
-1     272	1     -272
-2     136	2     -136
-4     68	4     -68
-8     34	8     -34
-16     17	16     -17

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

PRODUCT = -272 and SUM = 1
-1     272	1     -272
-2     136	2     -136
-4     68	4     -68
-8     34	8     -34
-16     17	16     -17

Step 4: Put -16 and 17 into placeholders to get factored form.

$$ \begin{aligned} x^{2}+x-272 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}+x-272 & = (x -16)(x + 17) \end{aligned} $$

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