Question

factor completely.
$2x^3 - 3x^2 + 8x - 12$

Explanation:

Step1: Group the terms

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

Step2: Factor out the GCF from each group

From the first group, the greatest common factor (GCF) of \(2x^3\) and \(-3x^2\) is \(x^2\). From the second group, the GCF of \(8x\) and \(-12\) is \(4\). Factoring these out, we get:
$$x^2(2x - 3) + 4(2x - 3)$$

Step3: Factor out the common binomial factor

Now, we can see that both terms have a common binomial factor of \((2x - 3)\). Factoring that out, we obtain:
$$(2x - 3)(x^2 + 4)$$

Answer:

\((2x - 3)(x^2 + 4)\)