Question

Write a third degree polynomial with -2 as its only zero

Answer 1

`p(x)=x^3+6x^2+12x+8`

Explanation:

It is given that -2 is the only zero of a third degree polynomial. That is

`x=-2`

And we can write it in factored form as

`x+2=0`

Since it is a third degree polynomial, so the multiplicity of -2 must be three. And therefore required polynomial is

`p(x)=(x+2)^3\\`

`p(x)=x^3+6x^2+12x+8`