Answer
$ \frac{1 }{ 2x^2} -3-2x^2.$
Work Step by Step
We divide each term of the polynomial by the monomial as follows
$$
\frac{1 - 6x^2 - 4x^4}{ 2x^2}= \frac{1 }{ 2x^2}+ \frac{ - 6x^2 }{ 2x^2}+ \frac{ - 4x^4}{ 2x^2} \\
= \frac{1 }{ 2x^2} -3-2x^2.
$$
