If the polynomial

By division algorithm we know,

Dividend = Divisor × Quotient + Remainder

Dividend − Remainder = Divisor × Quotient

x⁴ – 6x³ + 16x² – 25x + 10 – x – a = x⁴ – 6x³ + 16x² – 26x + 10 – a will be divisible by x² – 2x + k

It can be observed that (-10+2k)x +(10-a-8k+k²) will be zero.

Thus, (-10 + 2k) = 0 and (10 – a – 8k +k²) = 0

For (-10+2k) = 0 , 2k = 10 and thus k = 5

For (10 – a – 8k + k²) = 0

10 − a − 8 × 5 + 25 = 0

10 − a − 40 + 25 = 0

− 5 − a = 0

Therefore, a = −5

Hence, k = 5 and a = −5