While you are factoring a polynomial

So, I had a student that needed help during my working time, and I was helping her understand the concepts. I realized that there were so many hints and tricks that are so useful and easy to remember.  So, I'm going to be writing about the first one today which is if you have a negative midterm and a positive last number, that means that the number factors are both positive.  Now, you're probably wondering what I mean by this, so I'm going to be using an example to help explain what I am saying.

So we have this problem, right?

x^2-10x+24 (this reads x-square minus 10 plus 24)

So, being good math people, we're know that we first have to figure out the factors of 24 that is going to subtract (or you can think adding) that will give us a negative ten.  Well this is the first point that I made.  10 is a negative number, right?  And 24 is a positive number, so that means we're are going to have two negative factors, because we know that multiplying two negatives will give us a positive.  Well, the only factor that is going to subtract to give us a negative 10 is negative four and negative six, right?

Well, I hope you find this useful and can use this the next time you are factoring.

Introduction

Hello everyone! I'm starting this blog to give out little math tricks whenever you have to deal with a certain problem.  I hope that it's useful and that you can benefit from it!