remolatg

2021-02-25

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

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 $4{x}^{2}$.
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 $=\frac{-24{x}^{6}+36{x}^{8}}{4{x}^{2}}$.
Divide each term of the polynomial by the monomial $4{x}^{2}$.
$\frac{-24{x}^{6}+36{x}^{8}}{4}{x}^{2}=\left(-24\frac{{x}^{6}}{4}{x}^{2}\right)+\left(36\frac{{x}^{8}}{4}{x}^{2}\right)$
$\left(-24\frac{{x}^{6}}{4}{x}^{2}\right)+\left(36\frac{{x}^{8}}{4}{x}^{2}\right)=-6{x}^{4}+9{x}^{6}$
The simplified value of polynomial is $-6{x}^{4}+9{x}^{6}$.
Final statement:
The simplified value of polynomial after division is equals to $6{x}^{4}+9{x}^{6}$.

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