Factor polynomial $$ w^{2}+8w-180 $$

$$ w^{2}+8w-180 = ( w-10 )( w+18 ) $$

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:

$$ \color{blue}{ b = 8 } ~ \text{ and } ~ \color{red}{ c = -180 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ 8 } $ and multiply to $ \color{red}{ -180 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = -180 }$.

PRODUCT = -180
-1     180	1     -180
-2     90	2     -90
-3     60	3     -60
-4     45	4     -45
-5     36	5     -36
-6     30	6     -30
-9     20	9     -20
-10     18	10     -18
-12     15	12     -15

Step 3: Find out which pair sums up to $\color{blue}{ b = 8 }$

PRODUCT = -180 and SUM = 8
-1     180	1     -180
-2     90	2     -90
-3     60	3     -60
-4     45	4     -45
-5     36	5     -36
-6     30	6     -30
-9     20	9     -20
-10     18	10     -18
-12     15	12     -15

Step 4: Put -10 and 18 into placeholders to get factored form.

$$ \begin{aligned} w^{2}+8w-180 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ w^{2}+8w-180 & = (x -10)(x + 18) \end{aligned} $$

Polynomial Factoring Calculator