Step 1: Carothers equation.
Carothers equation relates the average degree of polymerization to the extent of reaction in step-growth (condensation) polymerization. It also helps predict gel formation during polymerization.
Step 2: Explanation of options.
- (A) Correct: Carothers equation applies to condensation (step-growth) polymerization.
- (B), (C), (D): These methods (chain growth) are not directly described by Carothers equation.
Final Answer: \[ \boxed{\text{A) condensation polymerization}} \]