# How do you divide (x^3+2x^2-11x-12)/(x^2-3x+2)?

Jun 25, 2016

Long divide coefficients to find:

$\frac{{x}^{3} + 2 {x}^{2} - 11 x - 12}{{x}^{2} - 3 x + 2} = x + 5 + \frac{2 x - 22}{{x}^{2} - 3 x + 2}$

#### Explanation:

You can just divide the coefficients like this:

The process is similar to long division of numbers.

Note that if there were any 'missing' powers of $x$ in the dividend or divisor then we would have to include $0$'s for them.

Write the dividend $1 , 2 , - 11 , - 12$ under the bar and the divisor $1 , - 3 , 2$ to the left.

Choose the first term $\textcolor{b l u e}{1}$ of the quotient so that when multiplied by the divisor, the resulting leading term ($1$) matches the leading term ($1$) of the dividend.

Write the product $1 , - 3 , 2$ of this first term of the quotient and the divisor under the dividend and subtract to give a remainder $5 , - 13$.

Bring down the next term $- 12$ from the dividend alongside it to give your running remainder $5 , - 13 , - 12$.

Choose the next term $\textcolor{b l u e}{5}$ of the quotient so that when multiplied by the divisor, the resulting leading term ($5$) matches the leading term ($5$) of the remainder.

Write the product $5 , - 15 , 10$ of this second term of the quotient and the divisor under the running remainder and subtract to give a remainder $2 , - 22$.

There are no more terms to bring down from the dividend, so this is our final remainder.

We find:

$\frac{{x}^{3} + 2 {x}^{2} - 11 x - 12}{{x}^{2} - 3 x + 2} = x + 5 + \frac{2 x - 22}{{x}^{2} - 3 x + 2}$