Posted by: mrswolfordmath7 on: November 12, 2008
Sample Quadratic: x2 + 8x + 16
Look at the last term (the constant-16). List its pairs of factors:
1 x 16
2 x 8
4 x 4
We need the pair that will add up to the coefficient of the second term (8).
This pair is 4 x 4 because 4 + 4 =8.
Since the first term is x2 it will factor into x * x.
Therefore, we can factor the trinomial into the following binomials: (x + 4)(x + 4).
We could check this by using FOIL (First, Outer, Inner, Last)
F: x * x = x2
O: x * 4 = 4x
I: 4 *x = 4x
L: 4 * 4 = 16
Then we add them to get: x2 + 4x + 4x + 16 = x2 + 8x + 16 (the original quadratic).
Yes, I really had to think about what I was doing instead of just going through the motions of solving the problem.
Unfortunately, it is not in my curriculum to teach factoring quadratics, but I could easily apply this to another concept. I could have students paraphrase the steps to solving a multi-step equation, or for adding or subtracting fractions with unlike denominators, etc…
November 12, 2008 at 3:08 pm
Jackie,
I thought your explanation was very easy to follow. As you probably have guessed, when you toss in negative coefficients or a problem where the coefficient of x-squared is not 1, the explanation gets very dicey.
For middle school, or even high school students, it is important to have a clear understanding of what the factors mean, have numerous examples, display graphs showing the roots, and use models, before definitions or rules are attempted.
Getting into quadratics in some detail, I think is an Algebra II topic. I would keep things very simple at the middle school level.
Tom