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

Question
Polynomial division
asked 2021-03-09
Perform the indicated divisions of polynomials by monomials.
\(\frac{14xy-16x^{2}y^{2}-20x^{3}y^{4}}{-xy}\)

Answers (1)

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 \(-14+16xy+20x^{2}y^{3}\).
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