floymdiT

2021-03-09

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

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

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