Question

question
solve for all values of ( x ) by factoring.
( x^2 - 4x - 32 = 0 )

Explanation:

Step1: Factor the quadratic expression

We need two numbers that multiply to $-32$ and add to $-4$. These numbers are $-8$ and $4$. So:
$x^2 - 4x - 32 = (x - 8)(x + 4) = 0$

Step2: Apply zero product property

Set each factor equal to 0:
$x - 8 = 0$ or $x + 4 = 0$

Step3: Solve for $x$

For $x - 8 = 0$, add 8 to both sides: $x = 8$
For $x + 4 = 0$, subtract 4 from both sides: $x = -4$

Answer:

$x = 8$ and $x = -4$