Factor completely. (Hint: Look for the pattern of a perfect square trinomial before using other methods.) Select "Prime" if the polynomial cannot be factored. \( 49+x^{2}-14 x= \)

The expression \( 49 + x^{2} - 14x \) can be reorganized as \( x^{2} - 14x + 49 \). This resembles the perfect square trinomial pattern \( (a - b)^{2} = a^{2} - 2ab + b^{2} \). Here, \( a = x \) and \( b = 7 \), giving us \( (x - 7)^{2} \) as the factored form. If you want to see this in action, you can simply expand \( (x - 7)(x - 7) \) to verify it. You’ll get back the original polynomial \( x^{2} - 14x + 49 \). Remember, recognizing these patterns can save loads of time and effort—so keep an eye out for them in various equations you encounter!