Question: frustration with factors in a polynomial

I subs (a^2=4b, expression) and get (1+b)*x^2+a*(1+b)*x+b(b-1)+2*b visually, (b+1) is a factor of the polynomial but the machine refuse to recognise this, I tried /(b+1), collect, expand and simplify and all failed. This is quite a frustration to new user who just want to get things done quickly!
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