Factoring Trinomials: Dealing with Variables

Question

I'm current working with Trinomials, doing things such as $2w^2 + 38w + 140$. I know how to solve this, however, I encountered a different type of problem, where the last term has a variable in it: $x^3 - 10x^2 + 21x$. I'm not sure how to solve it when the $x$ is in that $21$.

Answer 1

The first step for any factoring problem is to factor out the greatest common factor, in this case $x$.

So $x^3 + 10x^2 + 21x$, we can factor out $x$ to get $x(x^2+10x+21)$. Can you then factor the remaining expression using the methods you already know?

Answer 2

Before trying to factor trinomials, it's a good idea to see if you can find a common factor. In this case, $x^3-10x^2+21x$, it's easy to see that there's a common factor, $x$. Thus, you get $x(x^2-10x+21)$, and you can factor $x^2-10x+21$ using the tools for trinomials.