Q.14

### Asked by kaivankoshti7111.10sdatl | 6th Jul, 2020, 08:56: PM

Expert Answer:

### TO find the remainder os the polynomial using remainder theorem.
Given polynomial is P(x)=x^{3}+(kx+8)x+k
When P(x) is divided by x+1 and x-2, the remainders would be P(-1) and P(2)
P(-1) = (-1)^{3} + [k(-1) + 8](-1) + k = -1 + k - 8 + k = 2k - 9
P(2) = (2)^{3} + [k(2) + 8](2) + k = 8 + (2k + 8)2 + k = 8 + 4k + 16 + k = 5k + 24
Sum of these two remainders is 1
Therefore, 2k - 9 + 5k + 24 = 1
5k + 2k + 24 - 9 = 1
7k + 15 = 1
7k = -14
k = -2

^{3}+(kx+8)x+k

^{3}+ [k(-1) + 8](-1) + k = -1 + k - 8 + k = 2k - 9

^{3}+ [k(2) + 8](2) + k = 8 + (2k + 8)2 + k = 8 + 4k + 16 + k = 5k + 24

### Answered by Renu Varma | 7th Jul, 2020, 11:18: AM

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