## 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 …