Write a pseudocode of evaluating polynomial expression using Horner’s rule and perform complexity analysis (step by step). Apply it to evaluation the polynomial expression: (10) P(x) = 3x⁶+4x⁵+2x4+2x³+8x+9

Here's the pseudocode for evaluating a polynomial expression using Horner's rule:

function evaluatePolynomial(coefficients, x):
    n = length(coefficients)
    result = coefficients[n]
    
    for i = n - 1 to 0, decrementing i by 1:
        result = result * x + coefficients[i]
    
    return result
 

Now let's analyze the complexity of the algorithm step by step:

1. Assigning `n = length(coefficients)` takes constant time, O(1).

1. Initializing `result` with `coefficients[n]` takes constant time, O(1).

1. The `for` loop iterates `n - 1` times, where `n` is the length of the `coefficients` array. The loop starts from `n - 1` and decrements `i` by 1 until it reaches 0. Hence, the time complexity of the loop is O(n).

1. Inside the loop, the operations `result = result * x` and __________ ___ __________ ___ ______.
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