Factoring Quadratics
November 22, 2009When factoring a quadratic equation (ax2 + bx + c), one should remember that you are simply breaking a trinomial into its binomial factors. Following these steps will help you factor a quadratic equation:
Ex: x2 + 9x + 20
1. Look at the x2 term. If it does not have a coefficient, then each of the binomial factors will just have an x term, like such: (x + )(x + ).
2. Look at the constant (or c) in the equation, and determine each set of factors, like such: Factors of 20 = (1&20, 2&10, 4&5). Determine which set of factors’ sum is equal to b, the coefficient of the x term. In the above example, 4+5 = 9
3. So, one of the binomial factors will have a positive 4 and the other will have a positive 5, like such: (x+4)(x+5)
Paraphrasing the instructions gave me the opportunity to think through the process and make sure that I was not missing a step somewhere along the way. I think that by having your students journal their own understanding about a process helps them to realize if they have a strong understanding of the process and helps them to identify areas where they may still have some questions.
Very clear explanation. You were smart to keep it simple by having a=1
Great job. I like that you included examples at each step. I think that always makes it easier for students to understand the processes being described, especially when they are looking back through their notes after class.
-Nick
It makes sense to look at the first term and write it in, then the constant; however for what ever reason I factor the constant then the first term. Must be the way I learned it so many years ago.
Shirl
I think you have a unique ability to verbally describe things, all of your explanations including this one always make me rework my thoughts. Thanks for sharing your words!
Thank you! I really enjoyed this course; I hope you did too. Have a wonderful Holiday!