Question

factor completely.

$2x^3 + 3x^2 - 22x - 33$

Explanation:

Step1: Group terms for factoring

$(2x^3 + 3x^2) + (-22x - 33)$

Step2: Factor out GCF from each group

$x^2(2x + 3) - 11(2x + 3)$

Step3: Factor out common binomial

$(2x + 3)(x^2 - 11)$

Step4: Check for further factoring

$x^2 - 11$ is a difference of squares, so:
$(2x + 3)(x - \sqrt{11})(x + \sqrt{11})$

Answer:

$(2x + 3)(x - \sqrt{11})(x + \sqrt{11})$