Find a and b such that $x^2 + 8x + 7 = (x + a)(x + b)$ for all real values of $x$. Find $a$ and $b$ such that $x^2 + 8x + 7 = (x +  a)(x + b)$  for all real values of $x$.
That is what the question states, I think you should factor 
Any Ideas on how to begin?


Use $$x=\frac{-b\pm \sqrt{b^2 - 4ac}}{2a},\quad \textrm{where }ax^2+bx+c=0$$ 

which gives $x=-1 \textrm{ or } -7$ , so factorize will be $(x+1)(x+7)$.
