when (x^4 - 6.x^3 + 16.x^2 - 25. x + 10) is divided by( x^2 - 2.x + k)

the remainder is = x+a

find the values of k and a

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- Jul 3rd 2009, 03:03 AMjashansinghalimpossible question for me!!!!!
when (x^4 - 6.x^3 + 16.x^2 - 25. x + 10) is divided by( x^2 - 2.x + k)

the remainder is = x+a

find the values of k and a - Jul 3rd 2009, 03:26 AMSwlabr
There are, I am sure, many subtle ways of solving this problem, but the most obvious one which springs to mind is a simple cheat:

We know that where is some unknown polynomial and , , and are as above, because that's what division with a remainder means. So, simply substitute unknowns into the polynomial and then multiply out and pair off the coefficients, and you'll get your result. - Jul 3rd 2009, 03:29 AMProve It