Answer:
[tex]p(x)=-x^3-2x^2+5x+6.[/tex]
Step-by-step explanation:
If a cubic polynomial has zeros [tex]x_1,\ x_2,\ x_3,[/tex] then it has a form
[tex]p(x)=a(x-x_1)(x-x_2)(x-x_3).[/tex]
In your case, zeros are -3, -1 and 2, then the polynomial is
[tex]p(x)=a(x-(-3))(x-(-1))(x-2),\\ \\p(x)=a(x+3)(x+1)(x-2).[/tex]
If [tex]p(0)=6,[/tex] then
[tex]p(0)=a(0+3)(0+1)(0-2)=6,\\ \\-6a=6,\\ \\a=-1[/tex]
and
[tex]p(x)=-(x+3)(x+1)(x-2)=-x^3-2x^2+5x+6.[/tex]
