How do you factor #18x^3+9x^5-27x^2#?
1 Answer
Dec 22, 2015
Find:
as shown below...
Explanation:
Rearrange in standard order (descending powers of
#18x^3+9x^5-27x^2#
#=9x^5+18x^3-27x^2#
#=9x^2(x^3+2x-3)#
Next note that the sum of the coefficients of
#=9x^2(x-1)(x^2+x+3)#
The discriminant of the remaining quadratic factor is
If you still want to factor it further you can use Complex coefficients:
#(x^2+x+3) = (x+1/2)^2+(sqrt(11)/2)^2#
#= (x+1/2-sqrt(11)/2 i)(x+1/2+sqrt(11)/2 i)#