Use the definition of big- Theta to prove that 5x^4 + 2x^3 - 1 is Theta (x^4). Solution Big O notation characterizes functions according to their growth rates: different functions with the same growth rate may be represented using the same O notation. The order of the polynomial 5x4 +2x3 - 1 is 4. The letter O is used because the growth rate of a function is also referred to as order of the function.