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

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Answer 1 · 2016-01-05T23:27:27

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 #0#'s for any missing powers of #x#.

I like to long divide the coefficients, not forgetting to include #0#'s for any missing powers of #x#...

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This is similar to long division of numbers.

Reconstructing polynomials from the resulting sequences we find that the quotient is #x^3+x-1# with remainder #-15x+13#

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)#