Final answer:
In mathematical equations, the constant factor in a high-order term can be ignored because it becomes inconsequential compared to the dominant term as the values of the independent variable increase.
Step-by-step explanation:
In mathematical equations, the constant factor in a high-order term does not affect the overall behavior of the function. This is because the high-order term grows much faster than the constant factor, and as the values of the independent variable increase, the effect of the constant factor becomes negligible compared to the high-order term.
For example, consider the function f(x) = 3x^3 + 2x^2 + 5x. As x approaches infinity, the dominant term is 3x^3, and the constant term 5x becomes inconsequential. Therefore, we can ignore the constant factor of the high-order term when analyzing the behavior of a function.
This simplification allows us to focus on the most significant terms and gain a better understanding of the overall trend of the function.