Question

15 multiple answer 3 points
what are the zeros of the function $f(x)=x^3 - 2x^2 - 24x$. select all that apply
2
24
-4
-24
-2
4
0
-6
6
previous

Explanation:

Step1: Factor out common term

$f(x) = x(x^2 - 2x - 24)$

Step2: Factor quadratic expression

Find two numbers that multiply to $-24$ and add to $-2$: $-6$ and $4$.
$f(x) = x(x - 6)(x + 4)$

Step3: Set $f(x)=0$ and solve

$x = 0$, $x - 6 = 0 \implies x=6$, $x + 4 = 0 \implies x=-4$

Answer:

-4, 0, 6