Factor polynomial $$ 8c^{2}-40c+32 $$

$$ 8c^{2}-40c+32 = 8( c-1 )( c-4 ) $$

Step 1 :

After factoring out $ 8 $ we have:

$$ 8c^{2}-40c+32 = 8 ( c^{2}-5c+4 ) $$

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.

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

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