Answer:
[tex]p(x)=x^3+6x^2+12x+8[/tex]
Step-by-step explanation:
It is given that -2 is the only zero of a third degree polynomial. That is
[tex]x=-2[/tex]
And we can write it in factored form as
[tex]x+2=0[/tex]
Since it is a third degree polynomial, so the multiplicity of -2 must be three. And therefore required polynomial is
[tex]p(x)=(x+2)^3\\[/tex]
[tex]p(x)=x^3+6x^2+12x+8[/tex]
