# How do you divide (x^4-2x^3-2x^2+5x+3)/(x^2-3) ?

Aug 29, 2016

$\frac{{x}^{4} - 2 {x}^{3} - 2 {x}^{2} + 5 x + 3}{{x}^{2} - 3} = {x}^{2} - 2 x + 1 - \frac{x + 6}{{x}^{2} - 3}$

#### Explanation:

One way is to long divide the coefficients, not forgetting to include a $0$ for the coefficient of the missing $x$ term in the divisor...

We find:

$\frac{{x}^{4} - 2 {x}^{3} - 2 {x}^{2} + 5 x + 3}{{x}^{2} - 3} = {x}^{2} - 2 x + 1 - \frac{x + 6}{{x}^{2} - 3}$