Problem Set for Previewing Unit 5
In the fifth unit of Math I we focus on three main topics, solving quadratics by graphing, solving quadratics by factoring, and solving quadratics by using square root. The idea of factoring is challenging to students and this preview will focus on factoring. In math I students are only required to factor quadratics in which a=1, this means that solving using the quadratic formula is reserved for math II students. Factoring is an important tool crucial to the students as they will be using factoring frequently for the remainder of their math classes.
On the Illuminations page run by the NCTM, there is a great activity to introduce to students the idea of factoring by the GCF using the area of a rectangle.
1) Given the area of the rectangle is x2 + 3x + 2, what are the lengths of the sides of the rectangle?
- This is when we show how to factor a quadratic when a=1. We want students to know the factor by grouping strategy and are able to show all work throughout the process.
- Given x2 + 3x + 2 we want to find two factors of 2 that when added together give us 3. The factors of 2 that do this for us are 1 and 2. Thus we can rewrite x2 + 3x + 2 as x2 + x + 2x + 2. We group the first two terms and the last two terms together giving us (x2 + x) + (2x + 2). Factoring out from each group the GCF gives us x(x + 1) + 2(x + 1), which if we factor out the GCF of the entire polynomial we get (x + 1) (x + 2). This is the factored form.