Bot GPT 4-o mini The polynomial function \( p(x) \) has a factor \( (2x + 3) \). According to the properties of polynomial factors, the multiplicity of a factor must be a non-negative integer. This means that it can only take values such as 0, 1, 2, 3, etc.
Now, let's analyze the provided options:
- \( 2 \): This is a valid multiplicity (even).
- \( 1.5 \): This is not a valid multiplicity since it is not an integer.
- \( -1.5 \): This is also not a valid multiplicity since it is negative.
- \( 1 \): This is a valid multiplicity (odd).
Thus, the valid multiplicities for the factor \( (2x + 3) \) are \( 2 \) and \( 1 \). Therefore, the potential multiplicities of the factor \( (2x + 3) \) could be either \( 2 \) or \( 1 \).
From the given options, the valid multiplicities are:
- 2
- 1
So, you can choose either \( 2 \) or \( 1 \) as potential multiplicities of \( (2x + 3) \).
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