Divide (2n^3+4n^2+n)÷4n

$(2 n^{3} + 4 n^{2} + n) \div 4 n$

Rewrite the division as a fraction.

$\frac{2 n^{3} + 4 n^{2} + n}{4 n}$

Factor $n$ out of $2 n^{3} + 4 n^{2} + n$ .

Factor $n$ out of $2 n^{3}$ .

$\frac{n (2 n^{2}) + 4 n^{2} + n}{4 n}$

Factor $n$ out of $4 n^{2}$ .

$\frac{n (2 n^{2}) + n (4 n) + n}{4 n}$

Raise $n$ to the power of $1$ .

$\frac{n (2 n^{2}) + n (4 n) + n^{1}}{4 n}$

Factor $n$ out of $n^{1}$ .

$\frac{n (2 n^{2}) + n (4 n) + n \cdot 1}{4 n}$

Factor $n$ out of $n (2 n^{2}) + n (4 n)$ .

$\frac{n (2 n^{2} + 4 n) + n \cdot 1}{4 n}$

Factor $n$ out of $n (2 n^{2} + 4 n) + n \cdot 1$ .

$\frac{n (2 n^{2} + 4 n + 1)}{4 n}$

Cancel the common factor of $n$ .

Cancel the common factor.

$\frac{n (2 n^{2} + 4 n + 1)}{4 n}$

Rewrite the expression.

$\frac{2 n^{2} + 4 n + 1}{4}$

Split the fraction $\frac{2 n^{2} + 4 n + 1}{4}$ into two fractions.

$\frac{2 n^{2} + 4 n}{4} + \frac{1}{4}$

Split the fraction $\frac{2 n^{2} + 4 n}{4}$ into two fractions.

$\frac{2 n^{2}}{4} + \frac{4 n}{4} + \frac{1}{4}$

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2 n^{2}$ .

$\frac{2 (n^{2})}{4} + \frac{4 n}{4} + \frac{1}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$\frac{2 n^{2}}{2 \cdot 2} + \frac{4 n}{4} + \frac{1}{4}$

Cancel the common factor.

$\frac{2 n^{2}}{2 \cdot 2} + \frac{4 n}{4} + \frac{1}{4}$

Rewrite the expression.

$\frac{n^{2}}{2} + \frac{4 n}{4} + \frac{1}{4}$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{n^{2}}{2} + \frac{4 n}{4} + \frac{1}{4}$

Divide $n$ by $1$ .

$\frac{n^{2}}{2} + n + \frac{1}{4}$