# Solve the followin inequality and write answer using interval notation x^5-2x^4+27x^2-54x_>0need answer asap

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### 1 Answer

`x^5-2x^4+27x^2-54x > 0`

We can factor into

`x^5-2x^4+27x^2-54x=x(x^4-2x^3+27x-54)=x(x-2)(x^3+27)=x(x-2)(x+3)(x^2-3x+9)`

So when is

`x(x-2)(x+3)(x^2-3x+9) > 0`

`x^2-3x+9` is always positive and has no real roots. Vertex = `(1/3,73/3)` Up parabola.

so

when x>2 x, x-2 and x+3 are all positive so the polynomial is > 0

when 0<x<2 x, and x+3 are positive and x-2 is negative so polynomial is < 0

when -3<x<0 x+3 is positive and x and x-2 are negative so polynomial is > 0

when x<-3 x+3, x, x-2 are all negative so polynomial is < 0

So

`x^5 - 2x^4 + 27x^2 - 54 > 0` on (-3,0) U (2,oo)