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 \(\frac{-16x^{4}+32a^{3}-56a^{2}}{-8a}\)

Divide each term of the polynomial by the monomial —8a.

\(\frac{-16x^{4}+32a^{3}-56a^{2}}{-8a} = (\frac{-16x^{4}}{-8a})+(\frac{32a^{3}}{-8a})+(\frac{-56a^{2}}{-8a})\)

\((\frac{16x^{4}}{8a})-(\frac{32a^{3}}{8a})+(\frac{56a^{2}}{8a}) = 2a^{3}-4a^{2}+7a\).

The simplified value of the polynomial is \(2a^{3}-4a^{2}+7a\).

Final statement:

The simplified value of the polynomial after division is equals to \(2a^{3}-4a^{2}+7a\).

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 \(\frac{-16x^{4}+32a^{3}-56a^{2}}{-8a}\)

Divide each term of the polynomial by the monomial —8a.

\(\frac{-16x^{4}+32a^{3}-56a^{2}}{-8a} = (\frac{-16x^{4}}{-8a})+(\frac{32a^{3}}{-8a})+(\frac{-56a^{2}}{-8a})\)

\((\frac{16x^{4}}{8a})-(\frac{32a^{3}}{8a})+(\frac{56a^{2}}{8a}) = 2a^{3}-4a^{2}+7a\).

The simplified value of the polynomial is \(2a^{3}-4a^{2}+7a\).

Final statement:

The simplified value of the polynomial after division is equals to \(2a^{3}-4a^{2}+7a\).