Factor polynomial $$ w^{2}+13w+36 $$

$$ w^{2}+13w+36 = ( w+4 )( w+9 ) $$

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:

$$ \color{blue}{ b = 13 } ~ \text{ and } ~ \color{red}{ c = 36 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ 13 } $ and multiply to $ \color{red}{ 36 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = 36 }$.

PRODUCT = 36
1     36	-1     -36
2     18	-2     -18
3     12	-3     -12
4     9	-4     -9
6     6	-6     -6

Step 3: Find out which pair sums up to $\color{blue}{ b = 13 }$

PRODUCT = 36 and SUM = 13
1     36	-1     -36
2     18	-2     -18
3     12	-3     -12
4     9	-4     -9
6     6	-6     -6

Step 4: Put 4 and 9 into placeholders to get factored form.

$$ \begin{aligned} w^{2}+13w+36 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ w^{2}+13w+36 & = (x + 4)(x + 9) \end{aligned} $$

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