Answer
$P(x)=x(x-2)(x+4)$
Zeros: $-4, 0,2,$ all single.
Sketch:
Work Step by Step
Factor out x
$P(x)=x(x^{2}+2x-8)\\\\$
the quadratic can be factored by finding two factors of (-8) whose sum is 2.
These are $-2 $ and $4.$
$P(x)=x(x-2)(x+4)$
Zeros: $-4, 0,2,$ all single.
y-intercept:$ (0,0)$
The leading factor of a third degree polynomial is positive.
The end behavior is as for $x^{3}$ ($-\infty$ at the far left, $+\infty$ at the far right)..
Sketch:
On the far left, it rises from $-\infty,$
crosses x at $(-4,0)$, rises and turns
to cross x at $(0,0)$, falls and
turns to cross x again at $(0,2)$
and continues rising to the far right.
