Final answer:
To find the result of dividing x^3 - 4 by x + 2, one would use polynomial long division or synthetic division, subtracting multiples of (x + 2) from (x^3 - 4) until the remainder is less than the degree of x + 2.
Step-by-step explanation:
The result of dividing x^3 - 4 by x + 2 is obtained through polynomial long division or synthetic division. This process involves determining how many times the divisor (x + 2) fits into the dividend (x^3 - 4). You subtract multiples of the divisor from the dividend until you end up with a remainder that is of less degree than the divisor. In this case, the solution would provide a quadratic polynomial and possibly a remainder.
To perform the division, set up the long division by placing x^3 - 4 inside the division symbol and x + 2 outside. Then, follow the division steps: divide the leading term of the dividend by the leading term of the divisor, multiply the entire divisor by this result, subtract it from the dividend, and bring down the next term. Repeat these steps until the remainder is of less degree than the divisor.