Question

1. ( x^3 - 3x^2 - 4x + 12 )

Explanation:

Step1: Group terms

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

Step2: Factor out GCF from each group

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

Step3: Factor out common binomial factor

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

Step4: Factor difference of squares

Factor $x^2 - 4$ as a difference of squares: $(x - 3)(x - 2)(x + 2)$

Answer:

$(x - 3)(x - 2)(x + 2)$