Given that the expression 2x^3 + mx^2 + nx + c leaves the same remainder when divided by x -2 or by x+1 I prove that m+n =-6

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.

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step-by-step explanation: