Question

What are the zeros of the polynomial function? f(x)=x^3+x^2−9x−9

Answer 1

`\boxed{x=-1, \ x=-3, \ x=3}`

Explanation:

The zeros of a function are the values of x when f(x) = 0.

`x^3 +x^2-9x-9=0`

Factor left side of the equation.

`x^2(x +1)-9(x+1)=0`

Take (x+1) common.

`(x^2-9)(x+1)=0`

Set factors equal to 0.

First possibility:

`x^2 -9=0`

`x^2 =9`

`x=\± √(9)`

`x=\± 3`

`x=-3 \ \mathrm{or} \ x=3`

Second possibility:

`x+1=0`

`x=-1`

Answer 2

1: x = -1

2: x = 3

3: x = -3

Explanation:

f(x)=x^3+x^2−9x−9

f(x)=x^2(x+1) −9x−9

f(x) = x^2(x+1) - 9(x+1)

f(x)= (x+1)(x^2-9)

f(x) =(x+1)(x-3)(x+3)