Answer
$1,3$ and $-3$
Work Step by Step
The given function is
$\Rightarrow y=x^3-x^2-9x+9$
Substitute $0$ for $y$.
$\Rightarrow 0=x^3-x^2-9x+9$
Group the terms.
$\Rightarrow 0=(x^3-x^2)+(-9x+9)$
Factor each group.
$\Rightarrow 0=x^2(x-1)-9(x-1)$
Factor out $(x-1)$.
$\Rightarrow 0=(x-1)(x^2-9)$
$\Rightarrow 0=(x-1)(x^2-3^2)$
Use difference of two squares pattern.
$\Rightarrow 0=(x-1)(x-3)(x+3)$
Use zero product property.
$\Rightarrow x-1=0$ or $x-3=0$ or $x+3=0$
Solve for $x$.
$\Rightarrow x=1$ or $x=3$ or $x=-3$
Hence, the zeros of the function are $1,3$ and $-3$.
