Factor polynomial $$ 2x^{2}+10x+8 $$

$$ 2x^{2}+10x+8 = 2( x+1 )( x+4 ) $$

Step 1 :

After factoring out $ 2 $ we have:

$$ 2x^{2}+10x+8 = 2 ( x^{2}+5x+4 ) $$

Step 2 :

Step 2: 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:

$$ \color{blue}{ b = 5 } ~ \text{ and } ~ \color{red}{ c = 4 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ 5 } $ and multiply to $ \color{red}{ 4 } $.

Step 3: Find out pairs of numbers with a product of $\color{red}{ c = 4 }$.

PRODUCT = 4
1     4	-1     -4
2     2	-2     -2

Step 4: Find out which pair sums up to $\color{blue}{ b = 5 }$

PRODUCT = 4 and SUM = 5
1     4	-1     -4
2     2	-2     -2

Step 5: Put 1 and 4 into placeholders to get factored form.

$$ \begin{aligned} x^{2}+5x+4 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}+5x+4 & = (x + 1)(x + 4) \end{aligned} $$

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