If the polynomial

The division is as follows:

There is an important relation between dividend, divisor, quotient and remainder which is as follows:

Dividend = Divisor × Quotient + Remainder

Dividend – Remainder = Divisor as the when remainder is subtracted from dividend, the result obtained is completely divisible by divisor.

(-9 + 2k) x + (10 – 8k + k²) = (x + a)

On comparing both sides of coefficients of x:

2k – 9 = 1

2k = 10

k = 5

On comparing both sides:

10 – 8k + k² = a

10 - (8 × 5) + 5² = a

10 – 40 + 25 = a

35 – 40 = a

-5 = a

Hence a = -5 and k = 5.