Question
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) ?(1 point)Responses221.51.5−1.5negative 1.51
Answers
Answered by
GPT-4o mini
The expression (2x + 3) can be rewritten in terms of its root by setting it equal to zero:
\[ 2x + 3 = 0 \]
\[ 2x = -3 \]
\[ x = -\frac{3}{2} \]
The multiplicity of a factor in a polynomial function indicates how many times that factor appears in the polynomial. Multiplicities can be either positive integers or zero. However, the multiplicity cannot be a fraction, negative, or non-integer.
Given the choices:
- 2
- 1.5
- -1.5
- negative 1.5
- 1
The possible multiplicities of (2x + 3) must be a non-negative integer. Therefore, among the listed options, the values that could be valid multiplicities are:
- 2
- 1
However, both 1.5 and any negative values are not valid multiplicities for a polynomial factor.
Based on this analysis, the only multiplicities that could apply are:
- **1**
- **2**
Therefore, the possible multiplicity of (2x + 3) that fits within the criteria is **1** or **2**.
\[ 2x + 3 = 0 \]
\[ 2x = -3 \]
\[ x = -\frac{3}{2} \]
The multiplicity of a factor in a polynomial function indicates how many times that factor appears in the polynomial. Multiplicities can be either positive integers or zero. However, the multiplicity cannot be a fraction, negative, or non-integer.
Given the choices:
- 2
- 1.5
- -1.5
- negative 1.5
- 1
The possible multiplicities of (2x + 3) must be a non-negative integer. Therefore, among the listed options, the values that could be valid multiplicities are:
- 2
- 1
However, both 1.5 and any negative values are not valid multiplicities for a polynomial factor.
Based on this analysis, the only multiplicities that could apply are:
- **1**
- **2**
Therefore, the possible multiplicity of (2x + 3) that fits within the criteria is **1** or **2**.
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