**Solution:**

We know that,

Dividend = Divisor × Quotient + Remainder

⇒ Dividend – Remainder = Divisor × Quotient

⇒ Dividend – Remainder is always divisible by the divisor.

Now, it is given that *f*(*x*) when divided by *x* ^{2} – 2*x* + *k* leaves (*x *+ *a*) as remainder.

⇒ (4k – 25 + 16 – 2k)x + [10 – k(8 – k) ] = x + a

⇒ (2k – 9)x + [10 – 8k + k^{2} ] = x + a

On comparing both the sides, we get

2k – 9 = 1

⇒ 2k = 10

**∴ k = 5**

Also 10 – 8k + k^{2} = a

⇒ 10 – 8(5) + 5^{2} = a

⇒ 10 – 40 + 25 = a

**∴ a = – 5**