Factor polynomial $$ -15x^{3}+5x^{2}+220x $$

$$ -15x^{3}+5x^{2}+220x = ( -5 )x( x-4 )( 3x+11 ) $$

Step 1 :

After factoring out $ -5x $ we have:

$$ -15x^{3}+5x^{2}+220x = -5x ( 3x^{2}-x-44 ) $$

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:

$$ a = 3 , b = -1 ~ \text{ and } ~ c = -44 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 3 }$ by the constant term $\color{blue}{c = -44} $.

$$ a \cdot c = -132 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = -132 $ and add to $ b = -1 $.

Step 5: All pairs of numbers with a product of $ -132 $ are:

PRODUCT = -132
-1     132	1     -132
-2     66	2     -66
-3     44	3     -44
-4     33	4     -33
-6     22	6     -22
-11     12	11     -12

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

PRODUCT = -132 and SUM = -1
-1     132	1     -132
-2     66	2     -66
-3     44	3     -44
-4     33	4     -33
-6     22	6     -22
-11     12	11     -12

Step 7: Replace middle term $ -1 x $ with $ 11x-12x $:

$$ 3x^{2}-x-44 = 3x^{2}+11x-12x-44 $$

Step 8: Apply factoring by grouping. Factor $ x $ out of the first two terms and $ -4 $ out of the last two terms.

$$ 3x^{2}+11x-12x-44 = x\left(3x+11\right) -4\left(3x+11\right) = \left(x-4\right) \left(3x+11\right) $$

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