Answer :
Answer:
The given polynomial function describes the roots of the polynomial function is -2 with multiplicity 2,4 with multiplicity 1, and -1 with multiplicity 3
Step-by-step explanation:
Given polynomial function can be written as
[tex]f(x)=(x+2)^2(x+4)(x+1)^3[/tex]
The given polynomial function has roots [tex](x+2)^2,(x+4),(x+1)^3[/tex]
Therefore it can be written as
[tex](x+2)^2=0[/tex] , [tex](x+4)=0[/tex] and [tex](x+1)^3=0[/tex]
[tex](x+2)^2=0[/tex]
Therefore root -2 has mulitiplicity 2
[tex](x+4)=0[/tex],
Therefore root 4 has mulitiplicity 1
[tex](x+1)^3=0[/tex],
Therefore root -1 has mulitiplicity 3
Now combining all roots we get
The given polynomial function describes the roots of the polynomial function is -2 with multiplicity 2,4 with multiplicity 1, and -1 with multiplicity 3