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

Question

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 a​

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Mackenzie 3 months 2021-07-25T20:23:26+00:00 1 Answers 0 views 0

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    0
    2021-07-25T20:25:01+00:00

    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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