Question

question
factor to find all x-intercepts of the function.
$f(x) = x^3 - 3x^2 - 4x + 12$
answer attempt 1 out of 2
0 solution no solution
$x = $

Explanation:

Step1: Group terms for factoring

Group the first two terms and the last two terms: \( (x^3 - 3x^2) + (-4x + 12) \)

Step2: Factor out common factors from each group

Factor \( x^2 \) from the first group and \(-4\) from the second group: \( x^2(x - 3) - 4(x - 3) \)

Step3: Factor out the common binomial factor

Factor out \( (x - 3) \): \( (x - 3)(x^2 - 4) \)

Step4: Factor the difference of squares

Factor \( x^2 - 4 \) as \( (x - 2)(x + 2) \), so the fully factored form is \( (x - 3)(x - 2)(x + 2) \)

Step5: Find x-intercepts by setting f(x) = 0

Set each factor equal to zero: \( x - 3 = 0 \) or \( x - 2 = 0 \) or \( x + 2 = 0 \)
Solving these gives \( x = 3 \), \( x = 2 \), \( x = -2 \)

Answer:

\( x = -2, 2, 3 \)