What is factoring? Factoring is the process of reversing the distribution of terms.
For example, when you multiply y and (5 − y), you get 5y − y2. Reversing this, if you’re given 5y − y2, you can “factor out” a y to transform the expression into y(5 − y). Another way of thinking about factoring is that you’re pulling out a common factor that’s in every term and rewriting the expression as a product.
You can factor out many different things on the GRE: variables, variables with exponents, numbers, and expressions with more than one term, such as (y − 2) or (x + w). Here are some examples:
| t2 + t = t(t + 1) |
Factor out a t. Notice that a 1 remains behind when you factor a t out of a t. |
| 5k3 − 15k2 = 5k2(k − 3) |
Factor out a 5k2. |
| 21j + 35k = 7(3j + 5k) |
Factor out a 7; because the variables are different, you can’t factor out any variables. |
If you ever doubt whether you’ve factored correctly, just distribute back. For instance, t(t + 1) = t × t + t × 1 = t2 + t, so t(t + 1) is the correct factored form of t2 + t.
You might factor expressions for a variety of reasons. One common reason is to simplify an expression (the GRE complicates equations that are actually quite simple). The other reason, which will be discussed in more detail shortly, is to find possible values for a variable or combination of variables.
Factor the following expressions.
4 + 8t
5x + 25y
2x2 + 16x3