Question

Form a polynomial whose zeros and degree are given.

Zeros: -2, 2, 9; degree: 3
Type a polynomial with integer coefficients and a leading coefficient of 1 in the box below.

Answer 1

the polynomial is:
`\mathbf{x^3-9x^2-4x+36=0}`

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:

`(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`

So, the polynomial is:
`\mathbf{x^3-9x^2-4x+36=0}`