Question

1. solve by factoring: $x^2 - 7x + 12 = 0$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(12\) (the constant term) and add up to \(-7\) (the coefficient of \(x\)). The numbers are \(-3\) and \(-4\) since \((-3)\times(-4) = 12\) and \((-3)+(-4)=-7\).

Step2: Factor the quadratic

Using the two numbers, we can factor the quadratic equation \(x^{2}-7x + 12=0\) as \((x - 3)(x - 4)=0\).

Step3: Solve for \(x\)

Set each factor equal to zero:

• For \(x - 3=0\), we get \(x = 3\).
• For \(x - 4=0\), we get \(x = 4\).

Answer:

\(x = 3\) or \(x = 4\)