Question

if the polynomial x⁴-6x³ +16²-25x+10 is divided by another polynomial x²-2x-k find the remainder.​

Answer 1

Step-by-step explanation:

On dividing x4 - 6x3 - 16x2 - 25x + 10 by x2 - 2x + k

PLEASE REFER TO THE ATTACHED FILE FOR THE PROCESS!!

Remainder = (2k - 9)x - (8 - k)k + 10

But the remainder is given as x+a.

On comparing their coefficients,

2k - 9 = 1

⇒ k = 10

⇒ k = 5 and,

-(8 - k)k + 10 = a

⇒ a = -(8 - 5)5 + 10 = -15 + 10 = -5

Hence, k = 5 and a = -5