#1 isn't bad. Not knowing where to start on it points to some conceptual holes that should probably be filled in by your teacher, since the rest of algebra will only get worse.

Anywho, as an example what if we randomly guess a=1, b=4. [These are really random, not chosen with any foreknowledge]

Then x^2 + 2x + 3 ≡ (x + a)^2 +b = (x+1)^2+4 = x^2+2x+1+4 = x^2+2x+5.

Does x^2+2x+3=x^2+2x+5? No, since 3 != 5, so this guess didn't work. What guesses will work, and when? Can you write algebraic formulas for those conditions? Figure that out and you'll get it.


#2 is more interesting, though. But, if you know the quadratic equation (I assume it's a quadratic and that you just forgot a "+" sign) you can find appropriate k's from the discriminant really quickly. Again this points to some conceptual misunderstandings that probably shouldn't be glossed over.... I could give you the answer, yeah, and how to derive it, but that probably wouldn't help as much as getting someone to explain these things face-to-face with you. Then again if you can figure out the questions from these relatively vague hints you should be fine for the course.