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The minimum number of arithmetic operations required to evaluate the polynomial P(X) = X5 + 8X3 + X for a given value of X using only one temporary variable is
1. 8
2. 7
3. 6
4. 5

1 Answer

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Correct Answer - Option 3 : 6

P(X) = X5 + 8X3 + X

= X (X4 + 8X2 + 1)

= X (X (X3 + 8X) + 1)

= X (X (X (X2 + 8)) + 1)

= X (X (X (X (X) + 8)) + 1)

Let A be the temporary variable to store immediate results.

1. A = (X) * (X); A = X2

2. A = (A) + 8; A = X2 + 8

3. A = (X) * (A); A = X3 + 8X

4. A = (X) * (A); A = X4 + 8X2

5. A = (A) + 1; A = X4 + 8X2 + 1

6. A = (X) * (A); X5 + 8X3 + X

Therefore, the minimum number of arithmetic operations required = 6.

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