Factor polynomial $$ x^{2}+37x-650 $$

$$ x^{2}+37x-650 = ( x-13 )( x+50 ) $$

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:

$$ \color{blue}{ b = 37 } ~ \text{ and } ~ \color{red}{ c = -650 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ 37 } $ and multiply to $ \color{red}{ -650 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = -650 }$.

PRODUCT = -650
-1     650	1     -650
-2     325	2     -325
-5     130	5     -130
-10     65	10     -65
-13     50	13     -50
-25     26	25     -26

Step 3: Find out which pair sums up to $\color{blue}{ b = 37 }$

PRODUCT = -650 and SUM = 37
-1     650	1     -650
-2     325	2     -325
-5     130	5     -130
-10     65	10     -65
-13     50	13     -50
-25     26	25     -26

Step 4: Put -13 and 50 into placeholders to get factored form.

$$ \begin{aligned} x^{2}+37x-650 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}+37x-650 & = (x -13)(x + 50) \end{aligned} $$

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