# How do you divide #( x^5 - x^3 - x^2 - 17x - 15 )/(x^2 - 2 )#?

##### 1 Answer

Jan 5, 2016

Long divide the coefficients to find:

#(x^5-x^3-x^2-17x-15)/(x^2-2) = (x^3+x-1) + (-15x+13)/(x^2-2)#

...not forgetting to include

#### Explanation:

I like to long divide the coefficients, not forgetting to include

This is similar to long division of numbers.

Reconstructing polynomials from the resulting sequences we find that the quotient is

That is:

#(x^5-x^3-x^2-17x-15)/(x^2-2) = (x^3+x-1) + (-15x+13)/(x^2-2)#

Or if you prefer:

#(x^5-x^3-x^2-17x-15) = (x^2-2)(x^3+x-1) + (-15x+13)#