Question

state the roots of the polynomial: ( x^3 + 11x^2 + 24x ). (hint: graph)
0, -8, -3
8, 3
0, 8, 3
-8, -3

Explanation:

Step1: Factor out common term

Factor $x$ from the polynomial:
$x^3 + 11x^2 + 24x = x(x^2 + 11x + 24)$

Step2: Factor quadratic expression

Factor the quadratic $x^2 + 11x + 24$:
$x^2 + 11x + 24 = (x + 3)(x + 8)$

Step3: Set polynomial to 0

Set factored form equal to 0:
$x(x + 3)(x + 8) = 0$

Step4: Solve for x

Apply zero product property:
$x=0$, $x+3=0 \implies x=-3$, $x+8=0 \implies x=-8$

Answer:

0, -8, -3