Check the solution to "Perform the indicated divisions of polynomials by monomials...."

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Jaya Legge

Answered question

2021-02-19

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

Answer & Explanation

ensojadasH

Skilled2021-02-20Added 100 answers

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

9 a^{2} b^{2}

.
Simplify the terms which are under division.
Calculation:
Consider the polynomial

\frac{- 27 a^{3} b^{4} - 36 a^{2} b^{3} + 72 a^{2} b^{5}}{9 a^{2} b^{2}}

.
Divide each term of the polynomial by the monomial

9 a^{2} b^{2}

\frac{- 27 a^{3} b^{4} - 36 a^{2} b^{3} + 72 a^{2} b^{5}}{9 a^{2} b^{2}} = (- 27 a^{3} \frac{b^{4}}{9} a^{2} b^{2}) + (- 36 a^{2} \frac{b^{3}}{9} a^{2} b^{2}) + (72 a^{2} \frac{b^{5}}{9} a^{2} b^{2}) =

= 3 a b^{2} - 4 b + 8 b^{3}

The simplified value of the polynomial is

3 a b^{2} - 4 b + 8 b^{3}

.
Final statement:
The simplified value of the polynomial after division is equals to

3 a b^{2} - 4 b + 8 b^{3}

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