Factoring Quadratics
Find two numbers that multiply to c and add to b.
Concept
Reverse the FOIL
Expanding (x + p)(x + q) gives x² + (p + q)x + pq. So factoring runs that backwards: find p and q multiplying to the constant and adding to the middle coefficient.
Once factored, the zero-product property finishes it: if a product is zero, one of the factors is zero, so x = −p or x = −q.
x² + (p+q)x + pq = (x + p)(x + q)