Factor polynomial $$ 6x^{2}-36x+256 $$

$$ 6x^{2}-36x+256 = 2( 3x^{2}-18x+128 ) $$

Step 1 :

After factoring out $ 2 $ we have:

$$ 6x^{2}-36x+256 = 2 ( 3x^{2}-18x+128 ) $$

Step 2 :

Step 2: Identify constants $ a $ , $ b $ and $ c $.
$ a $ is a number in front of the $ x^2 $ term $ b $ is a number in front of the $ x $ term and $ c $ is a constant. In this case:

$$ a = 3 , b = -18 ~ \text{ and } ~ c = 128 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 3 }$ by the constant term $\color{blue}{c = 128} $.

$$ a \cdot c = 384 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = 384 $ and add to $ b = -18 $.

Step 5: All pairs of numbers with a product of $ 384 $ are:

PRODUCT = 384
1     384	-1     -384
2     192	-2     -192
3     128	-3     -128
4     96	-4     -96
6     64	-6     -64
8     48	-8     -48
12     32	-12     -32
16     24	-16     -24

Step 6: Find out which factor pair sums up to $\color{blue}{ b = -18 }$

Step 7: Because none of these pairs will give us a sum of $ \color{blue}{ -18 }$, we conclude the polynomial cannot be factored.

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