Question

factor the polynomial.
$x^{3}+2x^{2}+6x + 12$
$x^{3}+2x^{2}+6x + 12=\square$
(factor completely.)

Explanation:

Step1: Group terms into pairs

Group first two and last two terms:
$(x^3 + 2x^2) + (6x + 12)$

Step2: Factor out GCF from each group

Factor $x^2$ from first pair, 6 from second:
$x^2(x + 2) + 6(x + 2)$

Step3: Factor out common binomial

Factor out $(x + 2)$ from both terms:
$(x + 2)(x^2 + 6)$

Answer:

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