Second degree polynomials of the form ax² + bx + c (quadratic) are a special case in polynomial factoring.  It may be factored using a variety of methods.

By factoring, we mean finding the two binomials whose products will equal the originial second degree polynomial.  For example, x² + x - 2 in factored form is (x - 1)(x + 2).

There are several methods that may be used to factor second degree polynomials.

The first one involves using mental math to determine the factors of the polynomial, and is sometimes referred to as the reverse foil method.  This method works well when the "a" value in the quadratic equation is 1, but is more difficult when a is not 1.  A demonstration video of the mental math method when the "a" is one is shown on this page under the Type III Factoring heading.

Another method is to apply type IV factoring, factoring by grouping, to the polynomial.  We will call this method factoring by grouping.

Another method is the box method, that works well for any value of a, as does the diamond method, and the "slide and divide" method.

The notes provide further explanation and examples, as do these class notes.

This flowchart provides guidelines as to which method to use when factoring a second degree polynomial.