TITLE: Taking Calculus in a few days and I still don't know how to factorize quadratics
QUESTION [13 upvotes]: Taking Calculus in a few days and I still don't know how to factorize quadratics with a coefficient in front of the 'x' term. I just don't understand any explanation. My teacher gave up and said just use the formula to find the roots or something like that..
Can someone explain to me simply how I would step by step factorize something like $4x^2 + 16x - 19$ ?

REPLY [3 votes]: The way to factor any quadratic is to use the curious property of all quadratics that with the proper constant term, the quadratic would be a perfect square. The  first two terms determine what the necessary constant term would be. So get the necessary constant term by squaring the first two terms. Then add or subtract enough to both sides of the original equation to make the left side a square. Now we can take the square root of both sides. That's it. This is precisely how the formula for roots of a quadratic is generated.