Perform the indicated divisions of polynomials by monomials. frac{14xy-16x^{2}y^{2}-20x^{3}y^{4}}{-xy}

Polynomial division
Perform the indicated divisions of polynomials by monomials.
$$\frac{14xy-16x^{2}y^{2}-20x^{3}y^{4}}{-xy}$$

2021-03-10
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 —xy.
Simplify the terms which are under division.
Calculation:
Consider the polynomial $$\frac{14xy-16x^{2}y^{2}-20x^{3}y^{4}}{-xy}$$
Divide each term of the polynomial by the monomial -xy.
$$\frac{14xy-16x^{2}y^{2}-20x^{3}y^{4}}{-xy} =(\frac{14xy}{-xy})+(\frac{-16x^{2}}{-xy})+(\frac{-20x^{3}y^{4}}{-xy})$$
$$-(\frac{14xy}{-xy})+(\frac{-16x^{2}}{-xy})+(\frac{-20x^{3}y^{4}}{-xy}) = -14+16xy+20x^{2}y^{3}$$.
The simplified value of the polynomial is $$-14+16xy+20x^{2}y^{3}$$.
Final statement:
The simplified value of the polynomial after division is equals to $$-14+16xy+20x^{2}y^{3}$$.