g(x)=x^6+4x^5+4x^4

Question

g(x)=x^6+4x^5+4x^4

find the zeros and state the multiciplicites

Answer 1

x=0 has multiplicity 4

that leaves x^2+4x+4 which factors into (x+2)^2

x=-2 has multiplicity 2

just 2 zeros, 0 and -1, 1st with multiplicity 4 and 2nd with multiplicity 2