The multiplicity of a zero represents the number of times a factor is repeated in the factorization of the polynomial. If a graph crosses the x-axis at a certain zero, it means that the factor corresponding to that zero changes sign as it crosses the x-axis. In other words, the multiplicity must be an odd number.
Therefore, the multiplicity of a zero whose graph crosses the x-axis cannot be 2 (Option #1) or 4 (Option #3), since both of these are even numbers.
The only valid option is therefore Option #2: 3.
Which of the following could be the multiplicity of a zero whose graph crosses the x-axis?
Option #1: 2
Option #2: 3
Option #3: 4
1 answer