Question

If the polynomial X4- 6X3+16X2-25X+10 is divided by another polynomial X2-2X+k, the reminder is X+a . Find k and a

Answer 1

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

∴ a = – 5