 # Perform the indicated divisions of polynomials by monomials. (-27a^3b^4-36a^2b^3+72a^2b^5)/(9a^2b^2) Jaya Legge 2021-02-19 Answered

Perform the indicated divisions of polynomials by monomials.
$\frac{-27{a}^{3}{b}^{4}-36{a}^{2}{b}^{3}+72{a}^{2}{b}^{5}}{9{a}^{2}{b}^{2}}$

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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 trinomial.
To divide a polynomial by monomial, divide each term of the polynomial by the monomial.
Divide the trinomial by the monomial $9{a}^{2}{b}^{2}$.
Simplify the terms which are under division.
Calculation:
Consider the polynomial $\frac{-27{a}^{3}{b}^{4}-36{a}^{2}{b}^{3}+72{a}^{2}{b}^{5}}{9{a}^{2}{b}^{2}}$.
Divide each term of the polynomial by the monomial $9{a}^{2}{b}^{2}$.
$\frac{-27{a}^{3}{b}^{4}-36{a}^{2}{b}^{3}+72{a}^{2}{b}^{5}}{9{a}^{2}{b}^{2}}=\left(-27{a}^{3}\frac{{b}^{4}}{9}{a}^{2}{b}^{2}\right)+\left(-36{a}^{2}\frac{{b}^{3}}{9}{a}^{2}{b}^{2}\right)+\left(72{a}^{2}\frac{{b}^{5}}{9}{a}^{2}{b}^{2}\right)=$
$=3a{b}^{2}-4b+8{b}^{3}$
The simplified value of the polynomial is $3a{b}^{2}-4b+8{b}^{3}$.
Final statement:
The simplified value of the polynomial after division is equals to $3a{b}^{2}-4b+8{b}^{3}$.