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:

Given,

Divisor = x² – 2x + k

Dividend = x⁴ – 6x³ + 16x² – 25x + 10

Remainder = x + a

As we know that,

Dividend = divisor quotient + remainder

x⁴ – 6x³ + 16x² – 25x + 10 = x² – 2x + k quotient + (x + a)

x⁴ – 6x³ + 16x² – 25x + 10 – (x + a) = x² – 2x + k quotient

x⁴ – 6x³ + 16x² – 26x + 10 – a = quotient

x² – 2x + k

If the polynomial x⁴ – 6x³ + 16x² – 26x + 10 – a is divided by x² – 2x + k remainder comes out to be zero.

Therefore, By equating the remainder with zero, we have

(-10 + 2k) = 0 => 2k = 10 => k = 5

Or, 10 – a – 8k + k² = 0

Putting the value of k, we get

10 – a – 8(5) + (5)² = 0

10 – a – 40 + 25 = 0

- a – 5 = 0 => a = -5

Hence, k = 5 and a = -5

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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.

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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.

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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.