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 \(6x^{2}\)

Simplify the terms which are under division.

Calculation:

Consider the polynomial \(\frac{12x^{3}-24x^{2}}{6x^{2}}\).

Divide each term of the polynomial by the monomial \(6x^{2}\).

\(\frac{12x^{3}-24x^{2}}{6x^{2}} = (\frac{12x^{3}}{6x^{2}} - (\frac{24x^{2}}{6x^{2}}) = 2x-4\)

The simplified value of polynomial is \(2x — 4\).

Final statement:

The simplified value of polynomial after division is equals to \(2x-4\).

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 \(6x^{2}\)

Simplify the terms which are under division.

Calculation:

Consider the polynomial \(\frac{12x^{3}-24x^{2}}{6x^{2}}\).

Divide each term of the polynomial by the monomial \(6x^{2}\).

\(\frac{12x^{3}-24x^{2}}{6x^{2}} = (\frac{12x^{3}}{6x^{2}} - (\frac{24x^{2}}{6x^{2}}) = 2x-4\)

The simplified value of polynomial is \(2x — 4\).

Final statement:

The simplified value of polynomial after division is equals to \(2x-4\).