Factor polynomial $$ x^{2}-7x-30 $$

$$ x^{2}-7x-30 = ( x+3 )( x-10 ) $$

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:

$$ \color{blue}{ b = -7 } ~ \text{ and } ~ \color{red}{ c = -30 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ -7 } $ and multiply to $ \color{red}{ -30 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = -30 }$.

PRODUCT = -30
-1     30	1     -30
-2     15	2     -15
-3     10	3     -10
-5     6	5     -6

Step 3: Find out which pair sums up to $\color{blue}{ b = -7 }$

PRODUCT = -30 and SUM = -7
-1     30	1     -30
-2     15	2     -15
-3     10	3     -10
-5     6	5     -6

Step 4: Put 3 and -10 into placeholders to get factored form.

$$ \begin{aligned} x^{2}-7x-30 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}-7x-30 & = (x + 3)(x -10) \end{aligned} $$

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