Factoring Quadratics (x² + bx + c)

To factor x^2 + bx + c, find two numbers p and q such that: [formula] [formula] Then: x^2 + bx + c = (x + p)(x + q) It's like a puzzle: what two numbers multiply to c and add to b?

Example: Factor x^2 + 7x + 12

The signs in x^2 + bx + c tell you the signs of p and q: | b (sum) | c (product) | Signs of p and q | |---|---|---| | + | + | Both positive | | - | + | Both negative | | + | - | One positive, one negative (larger is positive) | | - | - | One positive, one negative (larger is negative) | This narrows down your search quickly.