Final answer:
The answer to whether synthetic division can always be used for dividing polynomials is False. Synthetic division is meant for divisors of the form x - k and cannot handle more complex divisors.
Step-by-step explanation:
The question asks if you can always use synthetic division for dividing polynomials. The answer is False. Synthetic division is a simplified form of polynomial division which can only be used when dividing a polynomial by a divisor of the form x - k, where k is a constant.
Synthetic division simplifies the process but is not versatile enough for all types of divisors. For example, it cannot be used when the divisor is a polynomial of degree higher than one, or if it has a leading coefficient other than 1. In such cases, long division must be used. Therefore, while synthetic division is a useful tool for certain division problems, it does not cover all cases.