Annette Arroyo

2021-02-12

Perform the indicated divisions of polynomials by monomials.
$\frac{-16{x}^{4}+32{a}^{3}-56{a}^{2}}{-8a}$

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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 -8a.
Simplify the terms which are under division.
Calculation:
Consider the polynomial $\frac{-16{x}^{4}+32{a}^{3}-56{a}^{2}}{-8a}$
Divide each term of the polynomial by the monomial —8a.
$\frac{-16{x}^{4}+32{a}^{3}-56{a}^{2}}{-8a}=\left(\frac{-16{x}^{4}}{-8a}\right)+\left(\frac{32{a}^{3}}{-8a}\right)+\left(\frac{-56{a}^{2}}{-8a}\right)$
$\left(\frac{16{x}^{4}}{8a}\right)-\left(\frac{32{a}^{3}}{8a}\right)+\left(\frac{56{a}^{2}}{8a}\right)=2{a}^{3}-4{a}^{2}+7a$.
The simplified value of the polynomial is $2{a}^{3}-4{a}^{2}+7a$.
Final statement:
The simplified value of the polynomial after division is equals to $2{a}^{3}-4{a}^{2}+7a$.

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