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

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

2021-02-26
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 $$6x^{4}+9x^{6}$$.

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