Question

$\bf \: If \: the \: polynomial \\ \: {x}^{4} - 6 {x}^{3} + 16 {x}^{2} - 25x + 10 \\ \bf \: is \: divided \: by \: another \: polynomial \\ {x}^{2} - 2x + k \: \bf \: the \: remainder \\ \bf \: comes \: out \: to \: be \: x + a \\ \\ Find \: k \: and \: a$

Answer 1

$\bf \:the \: solution \: is \: in \: the \: attachement$

Answer 2

Heya❗
Here's your answer❗

Given that the remainder is (x+a)

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

⇒ (2k - 9)x + [10 - 8k + k²] = x + a

On comparing both of 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⎟

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