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Divide. If there is a remainder, include it as a simplified fraction. $\newline$ $(6n^2 + 15n) \div 3n$

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Divide polynomials by monomials

Full solution

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

\newline

(6n^2 + 15n) \div 3n

Divide Expression: We have the expression to divide: $\newline$ $(6n^2 + 15n) \div 3n$ $\newline$ First, we will divide each term in the polynomial by the monomial $3n$ . $\newline$ $(6n^2 + 15n) \div 3n = \frac{6n^2}{3n} + \frac{15n}{3n}$
Divide First Term: Now let's divide the first term: $\newline$ $(6n^2)/(3n) = 6/3 \times n^2/n = 2n$ $\newline$ We simplify $6/3$ to $2$ and $n^2/n$ to $n$ .
Divide Second Term: Next, we divide the second term: $\newline$ $(15n)/(3n) = 15/3 \times n/n = 5$ $\newline$ We simplify $15/3$ to $5$ and $n/n$ to $1$ .
Write Result: Now we can write the result of the division: $\newline$ $(6n^2 + 15n) \div 3n = \frac{6n^2}{3n} + \frac{15n}{3n} = 2n + 5$

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