Question

If the polynomial x⁴ - 6x³ + 16x² - 25x + 10 is divided by another polynomial x² - 2x +k , the remainder comes out to be x+ a , find k and a ? ​

Answer 1

$\underline{\underline{\huge\mathfrak{your\:answer}}}$

k = 5

a = -5

step-by-step explanation:

on doing simple division,

the remainder we get is

(2k-9)x + (k^2-8k+10)

But it is given that,

remainder = x + a

=> (2k-9)x + (k^2-8k+10) = x+ a

on equatting the coefficients,

we get,

2k-9 = 1

=> k = 1+9/2

=> k = 10/2

=> k = 5

and

k^2 - 8k +10 = a

=> a = 5^2 -8×5 + 10

=> a = 25-40+10

=> a = -5

the division done is in the attachments.

kindly refer to it.

Answer 2

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