Factor by Grouping 2x^3+12x^2+8x+48

$2 x^{3} + 12 x^{2} + 8 x + 48$

Step 1

Factor out the GCF of $2$ from $2 x^{3} + 12 x^{2} + 8 x + 48$ .

Factor out the GCF of $2$ from each term in the polynomial.

Factor out the GCF of $2$ from the expression $2 x^{3}$ .

$2 (x^{3}) + 12 x^{2} + 8 x + 48$

Factor out the GCF of $2$ from the expression $12 x^{2}$ .

$2 (x^{3}) + 2 (6 x^{2}) + 8 x + 48$

Factor out the GCF of $2$ from the expression $8 x$ .

$2 (x^{3}) + 2 (6 x^{2}) + 2 (4 x) + 48$

Factor out the GCF of $2$ from the expression $48$ .

$2 (x^{3}) + 2 (6 x^{2}) + 2 (4 x) + 2 (24)$

Since all the terms share a common factor of $2$ , it can be factored out of each term.

$2 (x^{3} + 6 x^{2} + 4 x + 24)$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$2 ((x^{3} + 6 x^{2}) + 4 x + 24)$

Factor out the greatest common factor (GCF) from each group.

$2 (x^{2} (x + 6) + 4 (x + 6))$

Step 3

Factor the polynomial by factoring out the greatest common factor, $x + 6$ .

$2 ((x + 6) (x^{2} + 4))$