if the polynomial x^4 -6x^2 -25x+ 10 is divided by another polynomial x^2- 2x + k the remainder comes out to be x+ a , find k and

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1. Answer:

   The value of a for which (x

   4

   −x

   3

   −11x

   2

   +7x+a) is divisible by (x+3).

   We can find this by subtracting x=−3 in the polynomial and equate it to zero, since (x+3) is the root ( zero ) of the polynomial.

   ⇒(−3)

   4

   −(−3)

   3

   −11(−3)

   2

   +7(−3)+a=0

   ⇒81+27+9(−11)−21+a=0

   ⇒a=12.

   Hence, the answer is 12.

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