Question

factor completely. \\(12x^3 + 42x^2 - 14x - 49\\)

Explanation:

Step1: Group the terms

Group the first two terms and the last two terms:
$$(12x^3 + 42x^2) + (-14x - 49)$$

Step2: Factor out GCF from each group

Factor out $6x^2$ from the first group and $-7$ from the second group:
$$6x^2(2x + 7) - 7(2x + 7)$$

Step3: Factor out the common binomial factor

Now, factor out the common binomial factor $(2x + 7)$:
$$(6x^2 - 7)(2x + 7)$$

Answer:

$(6x^2 - 7)(2x + 7)$