A polynomial is an expression of one or more algebraic terms each of which consists of a constant multiplied by one or more variables raised to a non-negative integral power.

Here the given polynomial is a binomial.

To divide a polynomial by monomial, divide each term of the polynomial by the monomial.

Divide the binomial by the monomial \(4x^{2}\).

To divide a polynomial by monomial, divide each term of the polynomial by the monomial.

Simplify the terms which are under division.

Calculation:

Consider the polynomial \(=\frac{-24x^{6}+36x^{8}}{4x^{2}}\).

Divide each term of the polynomial by the monomial \(4x^{2}\).

\(\frac{-24x^{6}+36x^{8}}{4}x^{2}=(-24\frac{x^{6}}{4}x^{2})+(36\frac{x^{8}}{4}x^{2})\)

\((-24\frac{x^{6}}{4}x^{2})+(36\frac{x^{8}}{4}x^{2})=-6x^{4}+9x^{6}\)

The simplified value of polynomial is \(-6x^{4}+9x^{6}\).

Final statement:

The simplified value of polynomial after division is equals to \(6x^{4}+9x^{6}\).

Here the given polynomial is a binomial.

To divide a polynomial by monomial, divide each term of the polynomial by the monomial.

Divide the binomial by the monomial \(4x^{2}\).

To divide a polynomial by monomial, divide each term of the polynomial by the monomial.

Simplify the terms which are under division.

Calculation:

Consider the polynomial \(=\frac{-24x^{6}+36x^{8}}{4x^{2}}\).

Divide each term of the polynomial by the monomial \(4x^{2}\).

\(\frac{-24x^{6}+36x^{8}}{4}x^{2}=(-24\frac{x^{6}}{4}x^{2})+(36\frac{x^{8}}{4}x^{2})\)

\((-24\frac{x^{6}}{4}x^{2})+(36\frac{x^{8}}{4}x^{2})=-6x^{4}+9x^{6}\)

The simplified value of polynomial is \(-6x^{4}+9x^{6}\).

Final statement:

The simplified value of polynomial after division is equals to \(6x^{4}+9x^{6}\).