explain how to determine the end behavior of a polynomial.explain throughly with example(s)

as x gets huge, x^3 >> x^2 >> x

so
for example if y = 1x^4 + 5 x^3

well although 5 is much bigger than 1

(10^15)^4 = 10^60
5 (10^15)^3 = 5 *10^45 which is much, much smaller than 10^60
so as x goes to infinity, it is the highest power of x that counts.