1) Suppose $P(x)$ is a polynomial of smallest possible degree such that:
$\bullet$ $P(x)$ has rational coefficients
$\bullet$ $P(-3) = P(\sqrt 7) = P(1-\sqrt 6) = 0$
$\bullet$ $P(-1) = 8$
Determine the value of $P(0)$.
This is a degree of $3$, correct?
2) Find a monic quartic polynomial $f(x)$ with rational coefficients whose >roots include $x=3-i\sqrt[4]2$. Give your answer in expanded form.
How would I do this?