Step 1 :

After factoring out $ -1 $ we have:

$$ -6x^{2}-x+17 = - ~ ( 6x^{2}+x-17 ) $$

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:

$$ a = 6 , b = 1 ~ \text{ and } ~ c = -17 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 6 }$ by the constant term $\color{blue}{c = -17} $.

$$ a \cdot c = -102 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = -102 $ and add to $ b = 1 $.

Step 5: All pairs of numbers with a product of $ -102 $ are:

PRODUCT = -102
-1     102	1     -102
-2     51	2     -51
-3     34	3     -34
-6     17	6     -17

Step 6: Find out which factor pair sums up to $\color{blue}{ b = 1 }$

Step 7: Because none of these pairs will give us a sum of $ \color{blue}{ 1 }$, we conclude the polynomial cannot be factored.

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