Question

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

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

2021-02-13
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 $$2a^{3}-4a^{2}+7a$$.