A. Factoring

You are probably familiar with many processes that are reversible. Consider the following examples.

Process Outcome Reverse Process
Adding coloured flavour crystals to a cup of water. Coloured, flavoured water. Evaporation of the water will leave the coloured flavour crystals behind. Condensing the water vapor will bring the water back to its original state.
Opening an outside door in the winter. The temperature of the room is lowered in the immediate vicinity of the open door. Closing the door stops the cold air from entering and, in time, the air in the room will circulate through the heat source and bring the temperature back to normal.
Adding two hydrogen atoms to an oxygen atom. Water (H20) Through a process called electrolysis, water molecules can be separated into two hydrogen atoms and one oxygen atom.
Distributing 2x across the binomial (x − 5).

Factoring out what is common to both terms will result in the original product of monomial and binomial. 2x is common to both terms in the expression and is also known as the greatest common factor. Each term is divisible by 2x.

As you saw in the previous table, expanding (using the distributive property) and factoring polynomials, are reverse processes. You will use both factoring and expanding to change the format of quadratic functions in this lesson.

Recall that a number or an expression can be written as a product of its factors. If two numbers or expressions have the same factor, it is called a common factor. The largest possible factor of multiple numbers or expressions is called the greatest common factor (GCF).