Question

the sum of the remainders obtained when(x3+(k+8)x+k)is divided by (x-2) or whenit is divided by (x +1)is 0. find k (not using remainder theory

Answer 1

f(x)=x^3+(k+8)x+k,
g(x)= x-2
h(x)= x+1
Take x-2=0
x=2
f(2)=8+(k+8)2+k
=8+2k+16+k
=24+3k

Take x+1=0
x=-1
f(-1)=-1+(k+8)(-1)-5
=-1-k-8+k
=-9
Now, Add the remainders
3k+24-9=0
3k+15=0
k=-5
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