Question

If the polynomial x46x3+16x2_25x+10 is divided by
another polynomial x2–2x+k, the remainder comes out
to be x+a, find k and a.
m to the polynomial​

Answer 1

Step-by-step explanation:

Dividend = Divisor × Quotient + Remainder

⇒ Dividend – Remainder = Divisor × Quotient

⇒ Dividend – Remainder is always divisible by the divisor.

Now, it is given that f(x) when divided by x2 – 2x + k leaves (x + a) as remainder.

So, for f(x) to be completely divisible by x2 – 2x + k, remainder must be equal to zero

⇒ (–10 + 2k)x + (10 – a – 8k + k2) = 0

⇒ –10 + 2k = 0 and 10 – a – 8k + k2 = 0

⇒ k = 5 and 10 – a – 8 (5) + 52 = 0

⇒ k = 5 and – a – 5 = 0

⇒ k = 5 and a = –5