10.
6x^3 - x^2 -12x
Let’s go ahead and factor out an x:
x ( 6x^2 - x - 12)
Rewrite the 1st degree x as a difference of two values that have similar factors to 6 and 12:
x ( 6x^2 + 8x - 9x - 12 )
Factor out 2x from ( 6x^2 + 8x ):
x ( 2x ( 3x + 4) (-9x - 12) )
Factor out -3 from ( -9x - 12 ) to get the same:
x ( 2x ( 3x + 4 ) - 3 ( 3x + 4) )
Group these for your final factored form:
x (2x -3) (3x+4)
11.
Right off the bat, 8 is a factor of both 32 and 24, so divide these leading coefficients by 8:
8m^3n^2 - 32m^2n^3 + 24mn^4
m^3n^2 - 4m^2n^3 + 3mn^4
Factor out one m:
m ( m^2n^2 - 4mn^3 + 3n^4)
Now factor out an n^2:
mn^2 ( m^2 - 4mn + 3n^2)
This is the final factored form.
13.
Factor out an x:
x (2x^2 + 5x - 3)
Rewrite 5x as a difference of two terms that will factor well with 2 and 3:
x ( 2x^2 + 6x - x - 3)
Now factor out a 2x:
x ( 2x ( x + 3 ) - x - 3 )
Now factor the other part so that what’s left matches the previous factor:
x ( 2x (x + 3) -1 (x +3) )
Now group these for the final factored form:
x ( 2x - 1 ) ( x + 3 )