To factor the expression \( 14x^2 - 217 \), we start by identifying the common factors.
First, we can factor out the greatest common factor (GCF) of 14 from both terms:
\[ 14x^2 - 217 = 14(x^2 - \frac{217}{14}) \]
Next, we simplify \(\frac{217}{14}\):
\[ \frac{217}{14} = 15.5 \]
Thus, we can rewrite the expression as:
\[ 14(x^2 - 15.5) \]
However, \(15.5\) is not a perfect square, and the expression \(x^2 - 15.5\) does not factor nicely into rational factors.
If we want to express the quadratic as a difference of squares form, we could write:
\[ 14\left(x^2 - \left(\sqrt{15.5}\right)^2\right) \]
This form indicates that we could factor it further if we were to extend it to complex factors or keep it as is.
Thus, the expression \( 14x^2 - 217 \) can be factored as:
\[ 14(x^2 - 15.5) \]
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