Question

1. $x^2 - 3x - 4 = 0$

Explanation:

Step1: Factor the quadratic trinomial

Find two numbers that multiply to $-4$ and add to $-3$; these numbers are $-4$ and $1$.
$x^2 - 3x - 4 = (x - 4)(x + 1) = 0$

Step2: Apply zero product property

Set each factor equal to 0 and solve for $x$.
$x - 4 = 0$ or $x + 1 = 0$

Step3: Solve for $x$ in each equation

For $x - 4 = 0$, $x = 4$; for $x + 1 = 0$, $x = -1$.

Answer:

$x = 4$ or $x = -1$