Factor polynomial $$ n^{2}+3n-18 $$

$$ n^{2}+3n-18 = ( n-3 )( n+6 ) $$

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:

$$ \color{blue}{ b = 3 } ~ \text{ and } ~ \color{red}{ c = -18 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ 3 } $ and multiply to $ \color{red}{ -18 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = -18 }$.

PRODUCT = -18
-1     18	1     -18
-2     9	2     -9
-3     6	3     -6

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

PRODUCT = -18 and SUM = 3
-1     18	1     -18
-2     9	2     -9
-3     6	3     -6

Step 4: Put -3 and 6 into placeholders to get factored form.

$$ \begin{aligned} n^{2}+3n-18 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ n^{2}+3n-18 & = (x -3)(x + 6) \end{aligned} $$

Polynomial Factoring Calculator