Factoring Quadratics – in My Own Words

Quadratic Equation Example-  Ax² +Bx+C

In a quadratic equation, we have 3 terms. A, B, and C.  Our first term is x squared, our second term is a coefficient, and our third term is a constant term.  In order to factor a quadratic equation we must first determine the factors of the third term C.  Then we must determine out of those factors, which two can we add together to match our coefficient term.  Since our first term is squared we will start both binomials with x. (x+___)(x+__). Lets say that “B” is 5 and “C” is 6.  Since our two factors of six that we can add together are 2 and 3, we will complete our binomial with each term. Our final quadratic equation can be factored as this: (x+2)(x+3).  Using the foil method we would get x² +2x+3x+6. Now we combine the like terms we get x²+5x+6.

 

By paraphrasing the words from the “key information”, I was able to get a deeper understanding of how to factor a quadratic equation.  This was an interesting way to make the task more concrete.  I will use this method with my students in the final activity of my lesson in which we summarize the days concept by answering the essential question.

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