What is the time complexity of, f(n)= n3+n2+n+4

What is the time complexity of given function,
f(n)= n³+n²+n+4 ?

Solution:

Given,

f(n)= n³+n²+n+4

• f(n) >= n³+n²+n+4 
• f(n) >= n³+n²+n, for all n>=1
• f(n) >= n³+n² , for all n>=1
• f(n) >= n³, for all n>=1

Compare with the standard Big omega notation equation that is, 

f(n)>=c*g(n), for all n0>=n

Here,

g(n) = n3, 

c = 1

n₀ = 1

• f(n) = Ω(g(n))
• f(n) = Ω(n3)