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.
Vocabulary
Investigation
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.
Discussion Questions
1)
Given the area of the rectangle is x^{2}
+ 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 x^{2} + 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 x^{2} +
3x + 2 as x^{2} + x + 2x + 2. We
group the first two terms and the last two terms together giving us (x^{2}
+ 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.
From Kuta
Software there are many free worksheets with plenty of example problems to
work with students. This is Kuta Software’s worksheet on factoring.