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 \(-7x^{2}\).

Simplify the terms which are under division.

Calculation:

Consider the polynomial \(\frac{-35x^{5}-42x^{3}}{-7x^{2}}\)

Divide each term of the polynomial by the monomial \(-7x^{2}\).

\(\frac{-35x^{5}-42x^{3}}{-7x^{2}} = (\frac{-35x^{5}}{-7x^{2}})+(\frac{-42x^{3}}{-7x^{2}})\)

\((\frac{-35x^{5}}{-7x^{2}})+(\frac{-42x^{3}}{-7x^{2}})= 5x^{3}+6x\).

The simplified value of polynomial is \(5x^{3}+6x\).

Final statement:

The simplified value of the polynomial after division is equal to \(5x^{3}+6x\).

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 \(-7x^{2}\).

Simplify the terms which are under division.

Calculation:

Consider the polynomial \(\frac{-35x^{5}-42x^{3}}{-7x^{2}}\)

Divide each term of the polynomial by the monomial \(-7x^{2}\).

\(\frac{-35x^{5}-42x^{3}}{-7x^{2}} = (\frac{-35x^{5}}{-7x^{2}})+(\frac{-42x^{3}}{-7x^{2}})\)

\((\frac{-35x^{5}}{-7x^{2}})+(\frac{-42x^{3}}{-7x^{2}})= 5x^{3}+6x\).

The simplified value of polynomial is \(5x^{3}+6x\).

Final statement:

The simplified value of the polynomial after division is equal to \(5x^{3}+6x\).