Question

please solve this question

Answer 1

Answer:

k = -5

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Step-by-step explanation:

By the Remainder Theorem, the remainder when a polynomial is divided by (x-a) is simply the value of that polynomial at x=a.

So...

The remainder when x³ + (k+8)x + k is divided by (x-2) is

2³ + (k+8)×2 + k = 8 + 2k + 16 + k = 3k + 24.

The remainder when x³ + (k+8)x + k is divided by (x+1) = (x - (-1)) is

(-1)³ + (k+8)×(-1) + k = -1 -k -8 + k = -9.

The sum of the remainder is 0

=> 3k + 24 + (-9) = 0

=> 3k = -15

=> k = -5