Question

solve: $-x(x + 2)(x - 7) = 0$ $x = 0$, $x = -2$, or $x = 7$ solve these polynomial equations algebraically. solve: $2(x - 2)(x + 8)(x - 1.5) = 0$ solve: $-0.5(x + 1)(x + 3)(x + 11.2) = 0$ solve: $-\frac{2}{3}x(x + 9)(x - 6) = 0$

Explanation:

Step1: Apply Zero Product Property

Set each factor equal to 0:
$2=0$ (no solution), $x-2=0$, $x+8=0$, $x-1.5=0$

Step2: Solve for x in each equation

For $x-2=0$: $x=2$
For $x+8=0$: $x=-8$
For $x-1.5=0$: $x=1.5$

Step3: Apply Zero Product Property (second equation)

Set each factor equal to 0:
$-0.5=0$ (no solution), $x+1=0$, $x+3=0$, $x+11.2=0$

Step4: Solve for x in each equation

For $x+1=0$: $x=-1$
For $x+3=0$: $x=-3$
For $x+11.2=0$: $x=-11.2$

Step5: Apply Zero Product Property (third equation)

Set each factor equal to 0:
$-\frac{2}{3}=0$ (no solution), $x=0$, $x+9=0$, $x-6=0$

Step6: Solve for x in each equation

For $x+9=0$: $x=-9$
For $x-6=0$: $x=6$

Answer:

1. $x=2$, $x=-8$, or $x=1.5$
2. $x=-1$, $x=-3$, or $x=-11.2$
3. $x=0$, $x=-9$, or $x=6$