Consider the graph of the polynomial function p(x). Given that (2x+3) is a factor of p(x), which of the following could be the multiplicity of (2x+3) ?

Question

(1 point)
Responses

2
2

−1.5
negative 1.5

1
1

1.5

Answer 1

Since \( (2x + 3) \) is a factor of the polynomial function \( p(x) \), its multiplicity must be a non-negative integer. In polynomial functions, factors can have whole number multiplicities (1, 2, 3, ...) or zero, but never negative or non-integer multiplicities.

Given the options:

• 2 (valid)
• −1.5 (invalid)
• 1 (valid)
• 1.5 (invalid)

The possible multiplicities for the factor \( (2x + 3) \) are 2 or 1. Therefore, the valid responses regarding the multiplicity could be 2 or 1.