If the polynomial x4– 6x3 + 16x + 10 is divided by another polynomial x2 – 2x + k and the remainder obtained is (x + a), then find the values of k and a.
The division is as follows:
There is an important relation between dividend, divisor, quotient and remainder which is as follows:
Dividend = Divisor × Quotient + Remainder
Dividend – Remainder = Divisor as the when remainder is subtracted from dividend, the result obtained is completely divisible by divisor.
(-9 + 2k) x + (10 – 8k + k2) = (x + a)
On comparing both sides of coefficients of x:
2k – 9 = 1
2k = 10
k = 5
On comparing both sides:
10 – 8k + k2 = a
10 - (8 × 5) + 52 = a
10 – 40 + 25 = a
35 – 40 = a
-5 = a
Hence a = -5 and k = 5.
Couldn't generate an explanation.
Generated by AI. May contain inaccuracies — always verify with your textbook.
