Factoring Simple Expressions
Need some basic practice recognizing products and sums? Recognizing Products and Sums; Identifying Factors and Terms
Need some basic practice identifying common factors? Identifying Common Factors
That is, to factor an expression means to write the expression as a product.
The expression $\,ab + ac\,$ is a sum, since the last operation is addition. The expression $\,a(b + c)\,$ is a product, since the last operation is multiplication. The process of factoring took us from the sum $\,ab + ac\,$ to the product $\,a(b + c)\,.$
Notice that $\,\,ab + ac = a(b + c)\,\,$ is just the distributive law, backwards!
In going from the name $\,ab + ac\,$ to the name $\, a(b + c) \,,$ the common factor ($\,a\,$) is first identified, and written down. Next, an opening parenthesis ‘ ( ’ is inserted. Then, the remaining parts of each term are written down. Finally, the closing parenthesis ‘ ) ’ is inserted.
Note: In the exercises below, exponents are typed in using the ‘^’ key. For example, $\, x^2(5 - y^2) \,$ is typed in as: x^2(5 - y^2)
Note: The product $\,(2x+1)(x-3)\,$ can also be written as $\,(x-3)(2x+1)\,.$ There is no convention here about which name is ‘best’. The exercise below recognizes both answers.