Perform the indicated divisions of polynomials by monomials. frac{-24x^{6}+36x^{8}}{4x^{2}}

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 $6x^4+9x^6$.