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ICSE Class 10 Answered

using the reminder theorem find the reminder obtain when x cube +( kx + 8)X + k is divide by X + 1 and x minus 2 hands find k if the sum of two remainder is 1
Asked by tanaypatidar12345 | 25 Mar, 2022, 03:56: PM
Expert Answer
Let p(x) = x3 + (kx + 8)x + k = x3 + kx2 + 8x + k
When divided by (x + 1), the remainder is
p(-1) = -1 + k - 8 + k = 2k - 9
When divided by (x - 2), the remainder is
p(2) = 8 + 4k + 16 + k = 5k + 24
As sum of the remainders is 1, we have
p(-1) + p(2) = 1
i.e. 2k - 9 + 5k + 24 = 1
i.e. 7k + 15 = 1
i.e. 7k = -14
Therefore, k = -2 
Answered by Renu Varma | 28 Mar, 2022, 12:57: PM
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