How do you divide (-7x^3-5x^2-2x-4)/(x-4) ?

Jan 1, 2016

Long divide the coefficients to find:

$\frac{- 7 {x}^{3} - 5 {x}^{2} - 2 x - 4}{x - 4} = - 7 {x}^{2} - 33 x - 134 - \frac{540}{x - 4}$

The quotient is $- 7 {x}^{2} - 33 x - 134$ with remainder $- 540$

Explanation:

I like to long divide the coefficients like this:

The process is similar to long division of numbers.

In this particular example we find:

$\frac{- 7 {x}^{3} - 5 {x}^{2} - 2 x - 4}{x - 4} = - 7 {x}^{2} - 33 x - 134 - \frac{540}{x - 4}$

That is $\frac{- 7 {x}^{3} - 5 {x}^{2} - 2 x - 4}{x - 4}$ is $- 7 {x}^{2} - 33 x - 134$ with remainder $- 540$.

Or if you prefer:

$- 7 {x}^{3} - 5 {x}^{2} - 2 x - 4 = \left(- 7 {x}^{2} - 33 x - 134\right) \left(x - 4\right) - 540$