To check whether \(7 + 3x\) is a factor of \(3x^3 + 7x\), we can use polynomial long division. If the remainder is zero after dividing, then \(7 + 3x\) is a factor. Let's perform the division step by step.
### Step-by-Step Solution:
1. **Write the polynomials**: We have the dividend \(3x^3 + 7x\) and the divisor \(7 + 3x\).
2. **Rearrange the divisor**: It is often easier to work with the divisor in standard form. We can rewrite \(7 + 3x\) as \(3x + 7\).
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