Final answer:
The result of dividing x^3-6 by x+2, obtained through polynomial long division, is x^2-2x+4 with a remainder of -14/(x+2).
Step-by-step explanation:
Dividing a Polynomial by a Monomial
The question asks for the result of dividing x^3-6 by x+2. This process involves polynomial division, which can be performed either by long division or synthetic division. Since the divisor is a monomial (a polynomial with one term), we will use polynomial long division for this example.
Using these steps, we find that the quotient is x^2-2x+4 and the remainder is -14. So the complete answer to the division is x^2-2x+4 with a remainder of -14/(x+2).
Remember that when dividing exponents, you subtract the exponent of the denominator from the exponent of the numerator. Also, according to the rules of signs in division, when dividing two numbers with the same sign, the quotient will be positive, while dividing numbers with different signs will result in a negative quotient.