# 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.

S safeer

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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