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 the value
of k and a​

Answer 1

Answer:

$\bf \underline{✭Given:-}$

• P(x) = x⁴- 6x³ + 16x² - 25x + 10 (Dividend)
• Divisior = x² - 2x + k
• Remainder = x + a

$\bf \underline{✭To \: \: Find \: :-}$

• Value of k and a = ?

$\bf \underline{✭Solution:-}$

➝ 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

$\fbox \purple{Hence,Values of k = 12 and a = 422}$