Question

Ahoy!

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 be $x + a$
find the value of k and a.

Thanks =]

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