Question

1. ( x^2 + 8x + 12 = 0 )

Explanation:

Step1: Factor the quadratic trinomial

Find two numbers that multiply to 12 and add to 8, then rewrite the equation:
$(x + 2)(x + 6) = 0$

Step2: Apply zero product property

Set each factor equal to 0:
$x + 2 = 0$ or $x + 6 = 0$

Step3: Solve for x in each equation

For $x + 2 = 0$: $x = -2$; for $x + 6 = 0$: $x = -6$

Answer:

$x = -2$ or $x = -6$