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If the polynomials ax3 +3x2 -13 and 2x3 -5x +a when divided by (x – 2) leave the same remainder, find the value of a.

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Let p(x) = ax3 +3x2 -13 and q(x) = 2x3 -5x +a be the given polynomials.

The remainders when p(x) and q(x) are divided by (x-2) are p(2) and q(2).

By the given condition we have

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