Factor polynomial $$ x^{2}+30x+200 $$

$$ x^{2}+30x+200 = ( x+10 )( x+20 ) $$

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:

$$ \color{blue}{ b = 30 } ~ \text{ and } ~ \color{red}{ c = 200 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ 30 } $ and multiply to $ \color{red}{ 200 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = 200 }$.

PRODUCT = 200
1     200	-1     -200
2     100	-2     -100
4     50	-4     -50
5     40	-5     -40
8     25	-8     -25
10     20	-10     -20

Step 3: Find out which pair sums up to $\color{blue}{ b = 30 }$

PRODUCT = 200 and SUM = 30
1     200	-1     -200
2     100	-2     -100
4     50	-4     -50
5     40	-5     -40
8     25	-8     -25
10     20	-10     -20

Step 4: Put 10 and 20 into placeholders to get factored form.

$$ \begin{aligned} x^{2}+30x+200 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}+30x+200 & = (x + 10)(x + 20) \end{aligned} $$

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