Question

Perform the indicated divisions of polynomials by monomials. frac{-27a^{3}b^{4}-36a^{2}b^{3}+72a^{2}b^{5}}{9a^{2}b^{2}}

Polynomial division
ANSWERED
asked 2021-02-19
Perform the indicated divisions of polynomials by monomials.
\(\frac{-27a^{3}b^{4}-36a^{2}b^{3}+72a^{2}b^{5}}{9a^{2}b^{2}}\)

Expert Answers (1)

2021-02-20
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 \(9a^{2}b^{2}\).
Simplify the terms which are under division.
Calculation:
Consider the polynomial \(\frac{-27a^{3}b^{4}-36a^{2}b^{3}+72a^{2}b^{5}}{9a^{2}b^{2}}\).
Divide each term of the polynomial by the monomial \(9a^{2}b^{2}\).
\(\frac{-27a^{3}b^{4}-36a^{2}b^{3}+72a^{2}b^{5}}{9a^{2}b^{2}} = (-27a^{3}\frac{b^{4}}{9}a^{2}b^{2})+(-36a^{2}\frac{b^{3}}{9}a^{2}b^{2})+(72a^{2}\frac{b^{5}}{9}a^{2}b^{2})=\)
\(= 3ab^{2}-4b+8b^{3}\)
The simplified value of the polynomial is \(3ab^{2}-4b+8b^{3}\).
Final statement:
The simplified value of the polynomial after division is equals to \(3ab^{2}-4b+8b^{3}\).
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