if the polynomial x4-6x3+16x2-25x+10 is divided by another polynomial x2-2x+k, the remainder comes out to be x+a, find k and a

Asked by Ria Puri | 11th Apr, 2013, 04:02: PM

Expert Answer:

On using long division to divide the polynomial  x4-6x3+16x2-25x+10 by x2-2x+k, the remainder would be (-9+2k)x + 10-8k+k^2, however the remainder given is x+a
 
Hence comparing the coefficients, -9+2k = 1
k = 5
 
Also, a = 10-8k + k^2 = 10-40+25 = -5. 

Answered by  | 11th Apr, 2013, 05:37: PM

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