Perform the indicated divisions of polynomials by monomials. frac{-24x^{6}+36x^{8}}{4x^{2}}

Perform the indicated divisions of polynomials by monomials. frac{-24x^{6}+36x^{8}}{4x^{2}}

Question
Polynomial division
asked 2021-02-25
Perform the indicated divisions of polynomials by monomials. \(\frac{-24x^{6}+36x^{8}}{4x^{2}}\)

Answers (1)

2021-02-26
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 binomial by the monomial \(4x^{2}\).
To divide a polynomial by monomial, divide each term of the polynomial by the monomial.
Simplify the terms which are under division.
Calculation:
Consider the polynomial \(=\frac{-24x^{6}+36x^{8}}{4x^{2}}\).
Divide each term of the polynomial by the monomial \(4x^{2}\).
\(\frac{-24x^{6}+36x^{8}}{4}x^{2}=(-24\frac{x^{6}}{4}x^{2})+(36\frac{x^{8}}{4}x^{2})\)
\((-24\frac{x^{6}}{4}x^{2})+(36\frac{x^{8}}{4}x^{2})=-6x^{4}+9x^{6}\)
The simplified value of polynomial is \(-6x^{4}+9x^{6}\).
Final statement:
The simplified value of polynomial after division is equals to \(6x^{4}+9x^{6}\).
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