Step 1 :

After factoring out $ -1 $ we have:

$$ -2x^{2}+35x+23 = - ~ ( 2x^{2}-35x-23 ) $$

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:

$$ a = 2 , b = -35 ~ \text{ and } ~ c = -23 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 2 }$ by the constant term $\color{blue}{c = -23} $.

$$ a \cdot c = -46 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = -46 $ and add to $ b = -35 $.

Step 5: All pairs of numbers with a product of $ -46 $ are:

PRODUCT = -46
-1     46	1     -46
-2     23	2     -23

Step 6: Find out which factor pair sums up to $\color{blue}{ b = -35 }$

Step 7: Because none of these pairs will give us a sum of $ \color{blue}{ -35 }$, we conclude the polynomial cannot be factored.

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