Factoring Quadratics

Steps to factoring a quadratic expression in the form: x² + bx + c

1. Look at the third term, look at the factors of 8. (1×8, 2×4)

Paraphrased: Find all the sets of two numbers that equal “c” when multiplied together. Make sure that you identify whether “c” is positive or negative and choose number appropriately.

 

2. Which set of factors has the sum of b? 2 and 4

Paraphrased: Identify which set of numbers from step #1, equal “b” when added together, Let one of these numbers be represented by “d” and the other be represented by “e”

 

3. Look at the first term and factor it is (x * x) if so both binomials will start with x

Paraphrased: Write x² as a product of x and x. Each of these x’s represent the first terms in each of the binomials.

 

4. In one binomial, we will add 2 and in the other we will add 4. Therefore, we will have (x+2)(x+4)

Paraphrased: In one binomial we add “d” and the other we add “e”. The factored form of this trinomial will be (x+d)(x+e)

• Did paraphrasing the words help you internalize the concepts more?

Yes, just using words such as, “numbers whose product is…” or “numbers that multiply together…” makes the directions easier for me to follow. The term “factor” requires readers to have an understanding of the corresponding definition, as well as an understanding of the relation that the term factor has to the operation of multiplication.

• How can you apply this type of exercise in a lesson for your own students?

I think that it was a good exercise paraphrasing the steps, which I think students would benefit from also. I like the idea of giving notes on how to factor quadratic equations one day, without actually writing the numbered steps out. The next day I would have the students work in pairs to come up with what the actual steps to factoring are, as we had to do in this activity.