Question

Divide the polynomial x^4 - 6x^3 + 16x^2 - 25x + 10 by x^2 - 2x + k​

Answer 1

Answer:

a = – 5

Step-by-step explanation:

Given that the remainder is (x + a)

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

⇒ (2k – 9)x + [10 – 8k + k2 ] = x + a

On comparing both the sides, we get

2k  – 9 = 1

⇒ 2k = 10

∴ k = 5

Also 10 – 8k + k2 = a

⇒ 10 – 8(5) + 52 = a

⇒ 10 – 40 + 25 = a