To simplify the expression \(\frac{6x^2 + 20}{4}\), we can start by factoring the numerator.
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First, notice that both terms in the numerator share a common factor of 2: \[ 6x^2 + 20 = 2(3x^2 + 10) \]
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Now, we can rewrite the expression: \[ \frac{6x^2 + 20}{4} = \frac{2(3x^2 + 10)}{4} \]
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Simplify the fraction: \[ \frac{2(3x^2 + 10)}{4} = \frac{1}{2}(3x^2 + 10) \]
So the simplified expression is: \[ \frac{1}{2}(3x^2 + 10) \]
None of the options exactly match this simplified form, but if we were to conclude that it can be expressed in a different form or simplified further, it is important to note the denominator has not been eliminated entirely.
However, among the choices provided, if we break down the implications:
- The expression \(\frac{3x^2 + 10}{2}\) corresponds to the first option \(\frac{3x^2 + 10}{2}\).
Thus: The answer is: \(\frac{3x^2 + 10}{2}\) (this corresponds to the first option).