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If the polynomial x^4 – 6x^3 + 16x^2 – 25x + 10 is divided by another polynomial x^2 – 2x + k, the remainder comes out to be x + a, find k and a.

Q5   If the polynomial x ^4 - 6x ^3 + 16 x^2 - 35 x + 10  is divided by another polynomial x^2 - 2x + k,
        the remainder comes out to be x + a, find k and a.

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The polynomial division is carried out as follows

 Given the remainder =x+a

The obtained remainder after division is (2k-9)x+10-k(8-k)

now equating the coefficient of x

2k-9=1

which gives the value of k=5

now equating the constants

a=10-k(8-k)=10-5(8-5)=-5

Therefore k=5 and a=-5

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