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 the value
of k and a
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Answer:
- P(x) = x⁴- 6x³ + 16x² - 25x + 10 (Dividend)
- Divisior = x² - 2x + k
- Remainder = x + a
- Value of k and a = ?
➝ Firstly Dividing x⁴- 6x³ + 16x² - 25x + 10 by x² - 2x + k
➝ Refer to the attachment:-
Then,
➝ Remainder = (-23 + 2k)x + (k² + 24k + 10)
➝ Remainder (Given) :- x + a
✰ On Comparing the values of Coefficient of x
➛ -23 + 2k = 1
➛ 2k = 1+23
➛ 2k = 24
➛ k = 24/2
➛ k = 12
_______________________________
✰ On Comparing Constant term a
➛ k² + 24k + 10 = a
➛ (12)² + 24(12) + 10 = a
➛ 144 + 288 + 10 = a
➛ 422 = a
➛ a = 422
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