Question

find the solutions to this polynomial equation: 3(x - 2)(x² - 9)(x + 7) = 0. select all the correct answers. 2 -2 3

Explanation:

Step1: Factor the quadratic term

$x^2 - 9 = (x-3)(x+3)$
Equation becomes: $3(x-2)(x-3)(x+3)(x+7)=0$

Step2: Apply zero product property

Set each factor equal to 0:

1. $x-2=0$
2. $x-3=0$
3. $x+3=0$
4. $x+7=0$

Step3: Solve for x in each case

1. $x=2$
2. $x=3$
3. $x=-3$
4. $x=-7$

Answer:

2, 3