<s>[INST] Simple factorization problem I cannot find the solution! This is not a homework assignment. 

$11x^2+13x-7$

 [/INST] Do you know about completing squares? Write your expression as $$11\left(x^2+\frac{13}{11}x\right)-7.$$ The goal is to write this as a difference of squares, which is easy to factorise. To this end, complete the square on the expression in brackets, which becomes $$x^2+2x\frac{13}{22}+\left(\frac{13}{22}\right)^2-\left(\frac{13}{22}\right)^2=\left(x+\frac{13}{22}\right)^2-\left(\frac{13}{22}\right)^2.$$
Thus our expression becomes $$11\left(x+\frac{13}{22}\right)^2-11\left(\frac{13}{22}\right)^2-7=\left(\sqrt {11}\left(x+\frac{13}{22}\right)\right)^2-\frac{169}{44}-7=\left(\sqrt {11}\left(x+\frac{13}{22}\right)\right)^2-\left(\sqrt{\frac{477}{44}}\right)^2,$$ from where you should now be able to continue.
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