Factor polynomial $$ -15x^{6}-50x^{5}+40x^{4} $$

$$ -15x^{6}-50x^{5}+40x^{4} = ( -5 )x^{4}( 3x-2 )( x+4 ) $$

Step 1 :

After factoring out $ -5x^{4} $ we have:

$$ -15x^{6}-50x^{5}+40x^{4} = -5x^{4} ( 3x^{2}+10x-8 ) $$

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:

$$ a = 3 , b = 10 ~ \text{ and } ~ c = -8 $$

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

$$ a \cdot c = -24 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = -24 $ and add to $ b = 10 $.

Step 5: All pairs of numbers with a product of $ -24 $ are:

PRODUCT = -24
-1     24	1     -24
-2     12	2     -12
-3     8	3     -8
-4     6	4     -6

Step 6: Find out which factor pair sums up to $\color{blue}{ b = 10 }$

PRODUCT = -24 and SUM = 10
-1     24	1     -24
-2     12	2     -12
-3     8	3     -8
-4     6	4     -6

Step 7: Replace middle term $ 10 x $ with $ 12x-2x $:

$$ 3x^{2}+10x-8 = 3x^{2}+12x-2x-8 $$

Step 8: Apply factoring by grouping. Factor $ 3x $ out of the first two terms and $ -2 $ out of the last two terms.

$$ 3x^{2}+12x-2x-8 = 3x\left(x+4\right) -2\left(x+4\right) = \left(3x-2\right) \left(x+4\right) $$

Polynomial Factoring Calculator