Question

1. q. factor completely:

2x³ - 3x² -8x + 12

Explanation:

Step1: Group the terms

Group the first two terms and the last two terms: $(2x^3 - 3x^2) + (-8x + 12)$

Step2: Factor out GCF from each group

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

Step3: Factor out the common binomial factor

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

Step4: Factor the difference of squares

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

Answer:

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