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

Mar 25, 2017

The solution of the expression is: ${x}^{2} + x - 1 + \frac{2}{x - 3}$.

#### Explanation:

At first rewrite the expression into this form:
$\left({x}^{3} - 2 {x}^{2} - 4 x + 5\right)$:$\left(x - 3\right) =$

We will divide the term of the first polynomial by the first term in the second polynomial:
$\left({x}^{3} - 2 {x}^{2} - 4 x + 5\right)$:$\left(x - 3\right) = {x}^{2}$ , because ${x}^{3} / x = {x}^{2}$
Now we will multiply the second polynomial by our first term of the result and deduct it from the first polynomial:
$\left({x}^{3} - 2 {x}^{2} - 4 x + 5\right) - {x}^{2} \cdot \left(x - 3\right) = {x}^{2} - 4 x + 5$

We have a new polynomial ${x}^{2} - 4 x + 5$ and we have to do the same as in the first step:
$\left({x}^{2} - 4 x + 5\right)$:$\left(x - 3\right) = x$
Now multiply and deduct:
$\left({x}^{2} - 4 x + 5\right) - \left(x - 3\right) \cdot x = - x + 5$

$\left(- x + 5\right)$:$\left(x - 3\right) = - 1$
$\left(- x + 5\right) - \left(x - 3\right) \cdot \left(- 1\right) = 2$

The last term of the polynomial will be divided by the entire second polynomial:
$\frac{2}{x - 3}$

The final result is the sum of each result:
${x}^{2} + x - 1 + \frac{2}{x - 3}$