Factor polynomial $$ -19x^{3}-5x^{2}+8x $$

$$ -19x^{3}-5x^{2}+8x = -x( 19x^{2}+5x-8 ) $$

Step 1 :

After factoring out $ -x $ we have:

$$ -19x^{3}-5x^{2}+8x = -x ( 19x^{2}+5x-8 ) $$

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:

$$ a = 19 , b = 5 ~ \text{ and } ~ c = -8 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 19 }$ by the constant term $\color{blue}{c = -8} $.

$$ a \cdot c = -152 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = -152 $ and add to $ b = 5 $.

Step 5: All pairs of numbers with a product of $ -152 $ are:

PRODUCT = -152
-1     152	1     -152
-2     76	2     -76
-4     38	4     -38
-8     19	8     -19

Step 6: Find out which factor pair sums up to $\color{blue}{ b = 5 }$

Step 7: Because none of these pairs will give us a sum of $ \color{blue}{ 5 }$, we conclude the polynomial cannot be factored.

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