Question

Dividend- x^4-6x^3+16x^2-25x+10
Divisor - x^2-2x+k
Remainder - x+a
Find k and a using remainder theorem

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