Factor polynomial $$ n^{2}+3n-70 $$

$$ n^{2}+3n-70 = ( n-7 )( n+10 ) $$

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:

$$ \color{blue}{ b = 3 } ~ \text{ and } ~ \color{red}{ c = -70 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ 3 } $ and multiply to $ \color{red}{ -70 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = -70 }$.

PRODUCT = -70
-1     70	1     -70
-2     35	2     -35
-5     14	5     -14
-7     10	7     -10

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

PRODUCT = -70 and SUM = 3
-1     70	1     -70
-2     35	2     -35
-5     14	5     -14
-7     10	7     -10

Step 4: Put -7 and 10 into placeholders to get factored form.

$$ \begin{aligned} n^{2}+3n-70 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ n^{2}+3n-70 & = (x -7)(x + 10) \end{aligned} $$

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