It is shown that the symmetric behaviour of certain class
of knots can be realized by their polynomial representations.
We prove that every strongly invertible knot (open)
can be represented by a polynomial embedding $t\mapsto (f(t),g(t),h(t))$
of $\mathbb{R}$ in $\mathbb{R}^{3}$ where among the polynomials
$f(t)$, $g(t)$ and $h(t)$ two of them are odd polynomials
and one is an even polynomial. We also prove that a subclass
of strongly negative amphicheiral knots can be represented
by a polynomial embedding $t\mapsto(f(t),g(t),h(t))$ of $\mathbb{R}$
in $\mathbb{R}^{3}$ where all three polynomials $f(t)$, $g(t)$
and $h(t)$ are odd polynomials.