Algebra Practice Test

To determine which values are solutions to the equation x² - 9 = 0, we start by factoring the left side, which can be rewritten using the difference of squares:

x² - 9 = (x - 3)(x + 3) = 0.

For the product of two factors to equal zero, at least one of the factors must be zero. Therefore, we set each factor equal to zero:

1. x - 3 = 0 gives us x = 3.

2. x + 3 = 0 gives us x = -3.

Both values, 3 and -3, satisfy the original equation when substituted back:

- For x = 3:

(3)² - 9 = 9 - 9 = 0.

- For x = -3:

(-3)² - 9 = 9 - 9 = 0.

Since both solutions make the equation true, the correct answer is that both 3 and -3 are solutions to the equation. This is why the option indicating both values is the correct answer.