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Given:
The expression is:
It leaves the same remainder when divided by x -2 or by x+1.
To prove:
Solution:
Remainder theorem: If a polynomial P(x) is divided by (x-c), thent he remainder is P(c).
Let the given polynomial is:
It leaves the same remainder when divided by x -2 or by x+1. By using remainder theorem, we can say that
...(i)
Substituting in the given polynomial.
Substituting in the given polynomial.
Now, substitute the values of P(2) and P(-1) in (i), we get
Divide both sides by 3.
Hence proved.