The short version is that the fastest-growing term dominates all the others and for large xs the smaller terms round down to zero. Since big-O notation is about

The short version is that the fastest-growing term dominates all the others and for large xs the smaller terms round down to zero. Since big-O notation is about how the complexity grows for large inputs, you can assume the input is arbitrarily large, and you'll notice that the complexity is completely determined by the fastest-growing term. You drop the constant because it doesn't alter how the complexity grows as the input increases.