Construct a polynomial related with the roots of $f(x)=x^3+x^2+x-1$ Suppose $\lambda _1,\lambda _2,\lambda _3$ is the roots of $f(x)=x^3+x^2+x-1$, $g(x)=x^2+x+1$, solve for a polynomial $p(x)$ with rational coefficients such that $g\left(\lambda _1\right),g\left(\lambda _2\right),g\left(\lambda _3\right)$ is the root of it.
I have no idea, need some hints.
Seems I can get the result:  $\lambda _1\cdot \lambda _2\cdot \lambda _3$ is the factor of $-1$?
And polynomials of polynomials, I've only see that in the chapter of symmtric polynomials of my text.

For every root $\lambda$ of $f$, $\lambda\ne0$ and $g(\lambda)=1/\lambda$. Let $p(x)=1+x+x^2-x^3$. Then $f(x)=x^3p(1/x)$ hence for every such $\lambda$, $p(g(\lambda))=p(1/\lambda)=f(\lambda)/\lambda^3=0$, QED.
