Which of the following is a solution to the equation \( x^2 - 6x + 8 = 0 \)?

Which of the following is a solution to the equation \( x^2 - 6x + 8 = 0 \)?

• A. 1
• B. 2
• C. 3
• D. 4

Answer: (B)

To determine which value is a solution to the equation \( x^2 - 6x + 8 = 0 \), it is beneficial to factor the quadratic expression. This equation can be factored as follows: 1. Rewrite the quadratic expression in a factored form. We need two numbers that multiply to 8 (the constant term) and add up to -6 (the coefficient of the \( x \) term). The numbers that satisfy these conditions are -2 and -4, since \((-2) + (-4) = -6\) and \((-2) \times (-4) = 8\). 2. Thus, the equation factors to \((x - 2)(x - 4) = 0\). 3. Setting each factor to zero provides the potential solutions: - \(x - 2 = 0\) implies \(x = 2\), - \(x - 4 = 0\) implies \(x = 4\). Now, checking the provided choice of 2, we see that substituting \(x = 2\) back into the original equation yields: \[ (2)^2 - 6(2) +

To determine which value is a solution to the equation ( x^2 - 6x + 8 = 0 ), it is beneficial to factor the quadratic expression. This equation can be factored as follows:

1. Rewrite the quadratic expression in a factored form. We need two numbers that multiply to 8 (the constant term) and add up to -6 (the coefficient of the ( x ) term). The numbers that satisfy these conditions are -2 and -4, since ((-2) + (-4) = -6) and ((-2) \times (-4) = 8).

2. Thus, the equation factors to ((x - 2)(x - 4) = 0).

3. Setting each factor to zero provides the potential solutions:

• (x - 2 = 0) implies (x = 2),

• (x - 4 = 0) implies (x = 4).

Now, checking the provided choice of 2, we see that substituting (x = 2) back into the original equation yields:

[

(2)^2 - 6(2) +