Rui Baldwin

2021-03-08

Perform the indicated divisions of polynomials by monomials.
$\frac{13{x}^{3}-17{x}^{2}+28x}{-x}$

smallq9

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 —x.
Simplify the terms which are under division.
Calculation:
Consider the polynomial: $\frac{13{x}^{3}-17{x}^{2}+28x}{-x}$
Divide each term of the polynomial by the monomial —x.
$\frac{13{x}^{3}-17{x}^{2}+28x}{-x}=\left(12\frac{{x}^{3}}{-x}\right)+\left(-17\frac{{x}^{2}}{-x}\right)+\left(28\frac{x}{-x}\right)$
$=-\left(13\frac{{x}^{3}}{x}\right)+\left(-17\frac{{x}^{2}}{-x}\right)+\left(28\frac{x}{-x}\right)=-13{x}^{2}+17x-28$.
The simplified value of the polynomial is $-13{x}^{2}+17x-28$.
Final statement:
The simplified value of the polynomial after division is equals to $-13{x}^{2}+17x-28$.

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