To show that (x+2) is a factor, you can do polynomial long division to find the other factor (x^3 - 27). So x^4+2x^3−27x−54 = (x+2) * (x^3 - 27).
Be careful when you see "factor completely". That usually means that one of your factors can be factored some more. In this case, (x^3 - 27) is a difference of cubes, and can be factored more using the formula for that