By assuming that we are talking about polynomials with real coefficients. Suppose that the polynomials are,

$\mathrm{P(x)\; =\; axp+\; ...\; +\; bxq}$

$\mathrm{Q(x)\; =\; cxr+\; ...\; +\; dxs}$

Where . . . $\mathrm{Q(x)\; =\; cxr+\; ...\; +\; dxs}$