The given polynomial is expressed as
x^4-2x^3+x^2-8x-12
If we divide is by x^2 + 4 and there is no remainder, then x^2 + 4 is a factor. The division is shown below
For the division process, the first step was to divide x^4 by x^2 and this gace us x^2. We multiplied each term in x^2 + 0x + 4 by x^2 to get x^4 + 0x^3 + 4x^2. This was subtracted from the original polynomial. The process was repeated in the same manner till we got zero. This means that x^2 + 4 is a factor of x^4-2x^3+x^2-8x-12