waigaK

2020-11-10

Perform the indicated divisions of polynomials by monomials.
$\frac{-35{x}^{5}-42{x}^{3}}{-7{x}^{2}}$

cyhuddwyr9

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 binomial.
To divide a polynomial by monomial, divide each term of the polynomial by the monomial.
Divide the trinomial by the monomial $-7{x}^{2}$.
Simplify the terms which are under division.
Calculation:
Consider the polynomial $\frac{-35{x}^{5}-42{x}^{3}}{-7{x}^{2}}$
Divide each term of the polynomial by the monomial $-7{x}^{2}$.
$\frac{-35{x}^{5}-42{x}^{3}}{-7{x}^{2}}=\left(\frac{-35{x}^{5}}{-7{x}^{2}}\right)+\left(\frac{-42{x}^{3}}{-7{x}^{2}}\right)$
$\left(\frac{-35{x}^{5}}{-7{x}^{2}}\right)+\left(\frac{-42{x}^{3}}{-7{x}^{2}}\right)=5{x}^{3}+6x$.
The simplified value of polynomial is $5{x}^{3}+6x$.
Final statement:
The simplified value of the polynomial after division is equal to $5{x}^{3}+6x$.

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