Factor polynomial $$ -10n^{3}+35n^{2}-45n $$

$$ -10n^{3}+35n^{2}-45n = ( -5 )n( 2n^{2}-7n+9 ) $$

Step 1 :

After factoring out $ -5n $ we have:

$$ -10n^{3}+35n^{2}-45n = -5n ( 2n^{2}-7n+9 ) $$

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:

$$ a = 2 , b = -7 ~ \text{ and } ~ c = 9 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 2 }$ by the constant term $\color{blue}{c = 9} $.

$$ a \cdot c = 18 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = 18 $ and add to $ b = -7 $.

Step 5: All pairs of numbers with a product of $ 18 $ are:

PRODUCT = 18
1     18	-1     -18
2     9	-2     -9
3     6	-3     -6

Step 6: Find out which factor pair sums up to $\color{blue}{ b = -7 }$

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

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