# 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 x + a, find x and a.

## Solution :

Let us divide $$x^4 – 6x^3 + 16x^2 – 25x + 10$$ by $$x^2 – 2x + k$$

$$\therefore$$  Remainder = (2k – 9)x – (8 – k)k + 10

But the remainder is given as x + a,

On comparing their coefficients, we have :

2k – 9 = 1  $$\implies$$  k = 5

and -(8 – k)k + 10 = a

So, a = -(8 – 5)5 + 10

a = -15 + 10 = – 5

Hence, k = 5 and a = -5