To determine if the statement is true or false, we first need to solve the equation x² + 6x + 8 = 0. This is a quadratic equation which we can solve using factoring, the quadratic formula, or completing the square.
In this case, we can factor the equation. We look for two numbers that multiply to 8 (the constant term) and add up to 6 (the coefficient of x). The numbers 2 and 4 fit this requirement:
x² + 2x + 4x + 8 = (x + 2)(x + 4) = 0
Setting each factor to zero gives:
- x + 2 = 0 which simplifies to x = -2
- x + 4 = 0 which simplifies to x = -4
So, the solutions to the equation are x = -2 and x = -4. The original statement claims that the solutions are x = 4 or x = 2, which are not found in our factorization. Thus, the correct statement is:
False