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.