Simplify quantity 6 x squared plus 20 end quantity over 4.

quantity 3 x squared plus 10 end quantity over 2
quantity 3 x squared plus 20 end quantity over 2
6x + 5
x + 5

1 answer

To simplify the expression \(\frac{6x^2 + 20}{4}\), we can start by factoring the numerator.

  1. First, notice that both terms in the numerator share a common factor of 2: \[ 6x^2 + 20 = 2(3x^2 + 10) \]

  2. Now, we can rewrite the expression: \[ \frac{6x^2 + 20}{4} = \frac{2(3x^2 + 10)}{4} \]

  3. 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).