Question

Find all real solutions to the equation below.
Choices provided in image.

Answer 1

Given equation (x^2-9)(x+2)=0 ............(1)

By the zero product theorem, when the product of two factors is zero, at least one of the factors equals zero.

Therefore, the solutions of (1) are solutions of
(x^2-9)=0 and (x+2)=0

For (x^2-9)=0 factor (x+3)(x-3)=0 => x=3 or x=-3
For (x+2)=0 => x=-2

So the solution to equation (1) is S={3,-3,-2)
Which means that none of the first four answer options is correct.

Answer 2

(x^2 - 9)(x + 2) = 0
(x - 3)(x + 3)(x + 2) = 0

As any of the 3 above factors can equal zero the solutions are

x = 3, -3 , -2.

So the answer is E.