Factor completely 2x^3+4x^2+6x+12

2(x+2) (x^2+3)

Step-by-step explanation:

2x^3+4x^2+6x+12

I will use factor by grouping

2x^3+4x^2   +6x+12

Taking 2x^2 from the first two terms and 6 from the last two terms

2x^2( x+2)  +6(x+2)

Now I can factor x+2 out

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

We see in the last term that we can factor out 2

(x+2) 2(x^2+3)

Rearranging

2(x+2) (x^2+3)

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the diagram below is your final answer