Determine the most appropriate method and solve the following equation.
$x^2+6x+5=0$

• A. Factoring; $x=-1,x=-5$
• B. Quadratic Formula; $x=4.732,x=1.268$
• C. Factoring; $x=1,x=5$
• D. Quadratic Formula; $x=5,x=-1$

Answer: (A)

Verified step by step guidance

1. Identify the type of equation given: \(x^2 + 6x + 5 = 0\) is a quadratic equation because it is a polynomial of degree 2.
2. Determine the most appropriate method to solve the quadratic equation. Since the quadratic is in standard form and the coefficients are integers, try factoring first.
3. Look for two numbers that multiply to the constant term (5) and add up to the coefficient of the linear term (6). These numbers are 1 and 5 because \(1 \times 5 = 5\) and \$1 + 5 = 6$.
4. Rewrite the quadratic as a product of two binomials using these numbers: \((x + 1)(x + 5) = 0\).
5. Apply the Zero Product Property, which states if \(ab = 0\), then either \(a = 0\) or \(b = 0\). Set each factor equal to zero and solve for \(x\): \(x + 1 = 0\) and \(x + 5 = 0\).