How can you use factoring to solve quadratic equations in standard form?

An example will illustrate one method of doing this. Its called the 'ac' method.

Solve 2x^2 - 3x - 20 = 0

multiply the first and last numbers: - 2 * - 20 = - 40

Note that - 40 = - 8 * 5 and - 8 + 5 = - 3 (the 'middle' number in the standard form)

so we write:-

2x^2 - 8x + 5x - 20 = 0

2x (x - 4) + 5 (x - 4) = 0

(2x + 5) (x - 4) = 0

giving 2x + 5 = 0 or x - 4 = 0

giving the roots x = - 2.5 and x = 4