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?

By factorization,
$$x^2+8x+7 \equiv (x+7)(x+1) \equiv (x+a)(x+b)$$
$$\therefore \quad (a,b)=(1,7) \quad \text{or} \quad (7,1)$$
