Which division method is used for dividing polynomials by a polynomial, not limited to linear divisors?

• A. Rational Root Theorem
• B. The Polynomial Remainder Theorem
• C. Synthetic Division
• D. Polynomial Long Division

Answer: (D)

Dividing polynomials by another polynomial of any degree is done with polynomial long division. It works the same way as numerical long division: compare the leading terms, determine how many times the divisor fits into that leading part of the dividend, place that as the next term of the quotient, multiply the divisor by that term and subtract, then bring down the next terms and repeat until the remainder has degree less than the divisor. This method handles linear, quadratic, or higher-degree divisors.

Synthetic division is a faster shortcut, but it only works when the divisor is linear, specifically of the form x minus a constant. The Rational Root Theorem isn’t a division method at all; it’s about identifying possible rational roots. The Polynomial Remainder Theorem tells you the remainder when dividing by a linear divisor x minus c, but it doesn’t provide a general method for dividing by an arbitrary polynomial.