Solutions to 4 Degree Polynomial

I am trying to compute the solutions to $\displaystyle \mathrm{f(x)} = x^4 + 5x^3 - 9x^2 - 45x$

I factored all the way up to $\displaystyle \mathrm{f(0)} = (x+3)(x-3)(x^2 + 5x)$

Which gave me 3 out of 4 solutions $\displaystyle x = \{-5, -3, 3\}$

My book says the final solution is $\displaystyle 0$ but I don't see how they got that.

Re: Solutions to 4 Degree Polynomial

Rene

Factorise the last term x^2+5x =x(x+5) then you will find x = 0 the fourth root...................

the complete factorization is x(x-3)(x+3)(x+5) ...........

Re: Solutions to 4 Degree Polynomial

I'm such a dunce, thanks.