# Don’t Forget the One When Factoring

A very common mistake when factoring an algebraic expression is to “forget the 1”. For example, consider the following factoring problem: Factor ${x}^{2}+x$

We know that to factor means  to write multiple terms as a single term or a product. So ${x}^{2}+x$ which is two terms becomes a product if we write ${x}^{2}+x=x\left(x+1\right)$

So where did the 1 come from in $x+1$ ?  Probably the best way to answer this question is to realize the equation has to be reversible. What if $x\left(x+1\right)$ were the original problem?

What I mean is, if we start with $x\left(x+1\right)$ we get ${x}^{2}+x$ which was the original problem.