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Divide. If there is a remainder, include it as a simplified fraction. $(28h^8+8h^7+20h^6+8h^4)\div 4h^3$

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Divide polynomials by monomials

Full solution

Q. Divide. If there is a remainder, include it as a simplified fraction.

(28h^8+8h^7+20h^6+8h^4)\div 4h^3

Divide by $4h^3$ : We have the polynomial $(28h^8 + 8h^7 + 20h^6 + 8h^4)$ that we want to divide by the monomial $4h^3$ . We will divide each term of the polynomial by the monomial.
Divide $28h^8$ : First, divide the term $28h^8$ by $4h^3$ . $\newline$ $(28h^8) \div (4h^3) = 7h^5$
Divide $8h^7$ : Next, divide the term $8h^7$ by $4h^3$ . $\newline$ $(8h^7) \div (4h^3) = 2h^4$
Divide $20h^6$ : Then, divide the term $20h^6$ by $4h^3$ . $(20h^6) \div (4h^3) = 5h^3$
Divide $8h^4$ : Finally, divide the term $8h^4$ by $4h^3$ . $\frac{8h^4}{4h^3} = 2h$
Combine Results: Combine all the results from the previous steps to get the final answer. $\newline$ $(28h^8 + 8h^7 + 20h^6 + 8h^4) \div 4h^3 = 7h^5 + 2h^4 + 5h^3 + 2h$

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