Factor polynomial $$ 4x^{3}+40x^{2}+64x $$

$$ 4x^{3}+40x^{2}+64x = 4x( x+2 )( x+8 ) $$

Step 1 :

After factoring out $ 4x $ we have:

$$ 4x^{3}+40x^{2}+64x = 4x ( x^{2}+10x+16 ) $$

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:

$$ \color{blue}{ b = 10 } ~ \text{ and } ~ \color{red}{ c = 16 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ 10 } $ and multiply to $ \color{red}{ 16 } $.

Step 3: Find out pairs of numbers with a product of $\color{red}{ c = 16 }$.

PRODUCT = 16
1     16	-1     -16
2     8	-2     -8
4     4	-4     -4

Step 4: Find out which pair sums up to $\color{blue}{ b = 10 }$

PRODUCT = 16 and SUM = 10
1     16	-1     -16
2     8	-2     -8
4     4	-4     -4

Step 5: Put 2 and 8 into placeholders to get factored form.

$$ \begin{aligned} x^{2}+10x+16 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}+10x+16 & = (x + 2)(x + 8) \end{aligned} $$

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