Question

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

Answer 1

Answer:

1: x = -1

2: x = 3

3: x = -3

Step-by-step 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)

Answer 2

Answer:

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

Step-by-step 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:

$x^2 -9=0$

$x^2 =9$

$x=\± \sqrt{9}$

$x=\± 3$

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

Second possibility:

$x+1=0$

$x=-1$