the sum of the remainder obtained when(x^3 + (k + 8)x +k) is divided by (x - 2) or when it is divided by (x + 1) is zero . find the value of k
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x^3+(k+8)x+k=0
Because remainder is 0.
(x-2)is a factor of this and (x+1) is also a factor of this.
So,x=2,and,x=-1
if we put x=2 in this. then,
2^3+(k+8)2+k=0
=24+3k=0
=3(8+k)=0
=8+k=0
=k=-8
And if we put x=-1,then,
-1^3+(k+8)-1+k=0
=-1-k-8+k=0
=-9=0.
Which we does don't want.So k=-8
Because remainder is 0.
(x-2)is a factor of this and (x+1) is also a factor of this.
So,x=2,and,x=-1
if we put x=2 in this. then,
2^3+(k+8)2+k=0
=24+3k=0
=3(8+k)=0
=8+k=0
=k=-8
And if we put x=-1,then,
-1^3+(k+8)-1+k=0
=-1-k-8+k=0
=-9=0.
Which we does don't want.So k=-8
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