p(x) =xraise to 2 + x + k
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If (x+1) is a factor of function p(x) , then if we put x+1=0 i.e. x=-1 to the function p(x), then p(x) should become zero{This is called the remainder theorem.}
||| Remainder Theorem
If (x-r) is a factor of p(x), then p(r)=0 |||
Therefore, p(-1)=0
k(-1)^2-(-1)-4=0
k=3
ALTERNATIVELY,
On dividing (x+1) with p(x) we must get remainder=0 because (x+1) is a factor of p(x). So, it must completely divide p(x) without leaving a reminder.
On equating the remainder(which comes out to be in terms of k) equal to zero, we will get the same solution.
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