Final answer:
The zero with a multiplicity of 2 in the equation y=3x(x−4)³(x+6)²(2x+1) is x = -6. A zero's multiplicity is determined by the exponent of the factor in the polynomial equation.
Step-by-step explanation:
The zero in the equation y=3x(x−4)³(x+6)²(2x+1) with a multiplicity of 2 is x = -6. Multiplicity refers to the number of times a particular number is a root of the polynomial. In this equation, the factor (x−4) is raised to the third power, which means the zero x = 4 has a multiplicity of 3. The factor (x+6) is squared, indicating that the zero x = -6 has a multiplicity of 2. The other factors provide zeros with a multiplicity of 1. Therefore, the correct answer is C) x = -6.