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This same principle applies when there are more than two items in each factor; it just doesn't have a useful mnemonic word. Each term in the first factor (first parenthesized expression) get multiplied by each term in the second factor, and all the products are added up.
This same principle applies when there are more than two items in each factor; it just doesn't have a useful mnemonic word. Each term in the first factor (first parenthesized expression) get multiplied by each term in the second factor, and all the products are added up.
==Quadratic equations==
A quadratic equation is a type of equation in which the degree of x is exactly 2. Usually, these equations have two possible values of x. An example of a quadratic equation would be:
::<math>x^2 - 5x + 6 = 0\,</math>
There are several ways to solve quadratic equations. Let's look at three of the most common and use each to solve the above equation.
===Factoring===
Factoring is a method of solving quadratic equations that involves factoring the quadratic expression into smaller parts, and solving each part individually. It's often the fastest way to solve quadratics, if you can "see" the factors easily. In the case of our above equation, we can indeed factor it:
::<math>x^2 - 5x + 6 = (x - 2)(x - 3)\,</math>
Substituting the factored expression into the original equation yields:
::<math>(x - 2)(x - 3) = 0\,</math>
The key here is to recognize that if multiplying two or more numbers gives a result of zero, at least one of those numbers must itself equal zero. (It is impossible for there to be two nonzero numbers whose product is zero.) So the above equation can be split into two equations:
::<math>x - 2 = 0\,</math>
::<math>x - 3 = 0\,</math>
Thus x must equal either 2 or 3. There is no way to tell which is the "real" value of x, so the actual answer is written as:
::<math>x = 2, 3\,</math>
This is just shorthand for "x is either 2 or 3."
==Notes and references==
==Notes and references==