Question

# Perform the indicated divisions of polynomials by monomials. frac{-18x^{2}y^{2}+24x^{3}y^{2}-48x^{2}y^{3}}{6xy}

Polynomial division
Perform the indicated divisions of polynomials by monomials.
$$\frac{-18x^{2}y^{2}+24x^{3}y^{2}-48x^{2}y^{3}}{6xy}$$

2021-01-11
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 6xy.
Simplify the terms which are under division.
Calculation:
Consider the polynomial $$\frac{-18x^{2}y^{2}+24x^{3}y^{2}-48x^{2}y^{3}}{6xy}$$.
Divide each term of the polynomial by the monomial 6xy.
$$\frac{-18x^{2}y^{2}+24x^{3}y^{2}-48x^{2}y^{3}}{6xy} = (\frac{-18x^{2}y^{2}}{6xy})+(\frac{24x^{3}y^{2}}{6xy})+(\frac{-48x^{2}y^{3}}{6xy})$$
$$(\frac{-18x^{2}y^{2}}{6xy})+(\frac{24x^{3}y^{2}}{6xy})+(\frac{-48x^{2}y^{3}}{6xy}) = -3xy+4x^{2}y-8xy^{2}$$
The simplified value of the polynomial is $$-3xy+4x^{2}y-8xy^{2}$$.
Final statement:
The simplified value of the polynomial after division is equals to $$-3xy+4x^{2}y-8xy^{2}$$.