# How do you find the quotient of (12n^3-6n^2+15)div6n?

Jun 12, 2017

Quotient is $2 {n}^{2} - n$ and remainder is $15$

#### Explanation:

$\left(12 {n}^{3} - 6 {n}^{2} + 15\right) \div 6 n$

= $\frac{12 {n}^{3}}{6 n} - \frac{6 {n}^{2}}{6 n} + \frac{15}{6 n}$

= $2 {n}^{2} - n + \frac{15}{6 n}$

Hence Quotient is $2 {n}^{2} - n$ and remainder is $15$

Jun 12, 2017

$+ 2 {n}^{2} - n + \frac{15}{6 n}$

#### Explanation:

Note that I am using the place holder of $0 n$. It has no value.

$\textcolor{w h i t e}{.} \text{ } 12 {n}^{3} - 6 {n}^{2} + 0 n + 15$
color(magenta)(+2n^2)(6n)->" "ul(12n^3" "larr" Subtract")
$\text{ "0" } - 6 {n}^{2} + 0 n + 15$
color(magenta)(color(white)(2)-n)(6n)->" "ul(-6n^2" "larr" Subtract")
$\textcolor{m a \ge n t a}{\text{ "0" "+0n+15" "larr" Remainder}}$

$\textcolor{m a \ge n t a}{+ 2 {n}^{2} - n + \frac{15}{6 n}}$