Lesson 2.2: Factoring Polynomials
Completion requirements
You are probably familiar with many processes that are reversible. Consider the following examples.
As you saw in the last row of 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 equations of quadratic expressions in this lesson.
In Lesson 2.2, you will
| 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 \((x - 5)\). | \(2x^2 - 10x\) |
Factoring out what is common to both terms will result in the original factors of monomial and binomial. \(2x \) is common to both terms in the expression \(2x^2 - 10x\)
and is also known as the
greatest common factor. Each term
is divisible by \(2x\).
\(\begin{align} \frac{{2x^2 }}{{2x}} - \frac{{10x}}{{2x}} &= x - 5 \\ 2x^2 - 10x &= 2x\left( {x - 5} \right) \\ \end{align}\) |
As you saw in the last row of 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 equations of quadratic expressions in this lesson.
In Lesson 2.2, you will
-
factor polynomial expressions.