If $x^2 - 3x + 2$ is a factor of $x^4 - px^2 +q$, then find the value of $p$ and $q$ If $x^2 - 3x +2$ is a factor of $x^4-px^2+q$ then find the value of $p$ and $q$.
My attempt:
$$x^2-3x+2$$
$$x^2-2x-x+2$$
$$x(x-2)-1(x-2)$$
$$(x-1)(x-2)$$
How do I proceed further?
P.S: Edit after Deepak's comment!

Since $1$ and $2$ are zeros of $x^2 - 3x + 2$, they must also be zeros of $x^4-px^2+q.$

Substituting $x=1\,$ into $x^4-px^2+q\,$ yields $1-p+q = 0$.

Substituting $x=2\,$ into $x^4-px^2+q\,$ yields $16-4p+q = 0$.

So now you have two equations in two unknowns.
