Question

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Answer 1

REFER TO THE ATTACHMENT ❣️❣️

Answer 2

Solution :

Let, the given polynomial is

f(x) = x⁴ - 6x³ + 16x² - 25x + 10

g(x) = x² - 2x + k

Using long division method (check out the attachment), dividing f(x) by g(x), we get the remainder as

(- 9 + 2k)x + (10 - 8k + k²)

Given that,

(- 9 + 2k)x + (10 - 8k + k²) = x + a

Comparing among coefficients, we get

- 9 + 2k = 1

⇒ 2k = 10

⇒ k = 5

and 10 - 8k + k² = a

⇒ a = 10 - 8 (5) + 5²

⇒ a = 10 - 40 + 25

⇒ a = - 5

∴ k = 5 , a = - 5