Right, basically you base your value on the leading coefficient.
An easier way to explain it may be that:
will yield a "larger" infinity than .
So when that is subtracted, the value is still .
The on the end of the polynomial is irrelevant in this case.
Truthfully there is no such thing as a "larger" or "smaller" infinity, however this is an easier way to look at it.
Well basically,
But in general, you can use intuition on these limits. x^6 blows x^2 out of the water, no matter what the coefficient is on x^2, so -3x^2 doesn't matter as x gets huge (tends to infinity) and the plus 1 does not matter either when x is huge so in the long run, the polynomial acts exactly like x^6. and