Answer:
the polynomial is: [tex]\mathbf{x^3-9x^2-4x+36=0}[/tex]
Step-by-step explanation:
We need to form a polynomial whose zeros are:
-2,2,9
We can write them as: x=-2, x=2 and x=9
x+2=0, x-2=0 , x-9=0
(x+2)(x-2)(x-9)=0
Now multiplying all terms:
[tex](x(x-2)+2(x-2))(x-9)=0\\(x^2-2x+2x-4)(x-9)=0\\(x^2-4)(x-9)=0\\x^2(x-9)-4(x-9)=0\\x^3-9x^2-4x+36=0[/tex]
So, the polynomial is: [tex]\mathbf{x^3-9x^2-4x+36=0}[/tex]
