Factor polynomial $$ -9x^{2}+6x-19 $$

It seems that $ -9x^{2}+6x-19 $ cannot be factored out.

Step 1 :

After factoring out $ -1 $ we have:

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:

Step 3: Multiply the leading coefficient $\color{blue}{ a = 9 }$ by the constant term $\color{blue}{c = 19} $.

Step 4: Find out two numbers that multiply to $ a \cdot c = 171 $ and add to $ b = -6 $.

Step 5: All pairs of numbers with a product of $ 171 $ are:

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

Step 7: Because none of these pairs will give us a sum of $ \color{blue}{ -6 }$, we conclude the polynomial cannot be factored.