# 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)#