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Synthetic division is a simplified method of dividing a polynomial by a linear polynomial of the form x − a. It is a shorter alternative to the conventional polynomial long-division method. In synthetic division, only the coefficients of the polynomial are used, which makes the calculation quicker and easier.
It is commonly used to find the quotient and remainder when a polynomial is divided by x − a. It is also useful for checking roots and finding factors of a polynomial. If the remainder obtained from synthetic division is zero, then a is a root of the polynomial and x − a is a factor.
Here, synthetic division can be used because the divisor x − 2 is a linear polynomial of the form x − a.