Final answer:
The expression (x³ - 27) divided by (x - 3) is solved using synthetic division, leading to a quotient of x² + 3x + 9, which corresponds to option a).
Step-by-step explanation:
To solve the given expression (x³ - 27) ÷ (x - 3) using synthetic division, we set up our synthetic division table with the divisor x - 3 by using the root of the divisor, which is 3. The coefficients of x³, x², x, and the constant term are 1, 0, 0, and -27, respectively, for the dividend. We then bring down the leading coefficient, multiply it by our root, and proceed with the synthetic division process until we have our result.
The synthetic division would look like this:
3 | 1 0 0 -27
| 3 9 27
----------------
1 3 9 0
The solution to the division is x² + 3x + 9, which matches option a).