Question:- Factorize x^{2}+49 ?
This is certainly equal to the original formula but I would not consider it "factoring". I agree with MarkFL. Since the equation $\displaystyle x^2+ 49= 0$ has no real roots, $\displaystyle x^2+ 49$ pr $\displaystyle x^2= -49$ cannot be factored using real coefficients. But it can be factored as $\displaystyle (x- 7i)(x+ 7i)$ since, if $\displaystyle x^2= -49$, then $\displaystyle x= \pm 7i$.