Thread: impossible 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

Originally Posted by jashansinghal

When is divided by the remainder is find the values of k and a

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.

Originally Posted by jashansinghal

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

After using long division, you should find

.


So the remainder is:

.


Equating like co-efficients of gives

and .


Solving for in the first equation gives:



.


Substituting into the second equation gives:





.



So and .