Solve the equation $x^4-8x^3+23x^2-30x+15=0$ Solve the equation $$x^4-8x^3+23x^2-30x+15=0$$
As $x=0$ is obviously not a solution, we can consider $x\ne0$, so I have tried to divide both sides by $x^2$ to get $$x^2-8x+23-\dfrac{30}{x}+\dfrac{15}{x^2}=0$$ Clearly this does not help. I have also tried to find the rational roots using Horner's method. It seems that the polynomial in the left-hand side does not have rational roots.

Note that, if $p(x)$ is your polynomial, then $p(x+2)=x^4-x^2-2x-1=x^4-(x+1)^2$. Can you take it from here?
