UNIT 2 - Quadratic Mechanics - Factoring + Simplifying Rational Variable Expressions
UNIT 2 - Quadratic Mechanics - Factoring + Simplifying Rational Variable Expressions
In this unit we learn about the mechanics of switching between two of the forms of a quadratic. We will learn in unit 3 and 4 what each form is used best for.
Factored Form —> Standard Form - Expansion (Multiplying)
y=(x-s)(x-t) —> y=ax^2 + bx + c
Standard Form —> Factored Form - Factoring (Division) - This is the majority of the unit
y=ax^2 + bx + c —> y=(x-s)(x-t)
Lesson 2.1
In this lesson we explore the opposite process of factoring, expansion (multiplying). We will see that it is a means for checking whether our factoring work is correct as the unit progresses.
Lesson 2.2
In this lesson we will be looking at the number of terms in a polynomial, and removing any commonalities between them. We reference this as finding the greatest common factor for the rest of the unit.
Lesson 2.3
In this lesson we learn how to apply our common factoring skills from last lesson in a different situation. Factoring by grouping is exactly as it sounds. We group terms based on some similarity, and then remove that said familiarity to yield a simplified version of the original expression. This forms the basis for the process used in lesson 2.5, very important!
This formative exposes students to the kinds of questions they can expect on the test from lessons 2.1-2.3. We also model the expectations for what is required in a solution.
Formative 2.1-2.3 Checklist
Blank Formative
Formative 2.1-2.3 Video
Formative
2.1-2.3
Lesson 2.4
In this lesson we look at factoring simple trinomials where the “a-value” in y=ax^2 + bx + c is 1. We explore looking for numbers (factors) that satisfy both a multiplying and adding condition. Once these factors are found we can write the quadratic in factored form.
Blank Lesson
Lesson 2.4 Video
Lesson 2.5
In this lesson we explore the connections between lesson 2.3 (factoring by grouping), and lesson 2.4 (simple trinomials). We will create our M.A.N conditions, look for factors that satisfy said conditions, and then apply a process known as decomposition which uses our factoring by grouping skills.
Blank Lesson
Lesson 2.5 Video
Lesson 2.6
In this lesson we learn to identify special kinds of polynomials that can be factored in unique, more efficient ways. We will be looking at perfect square trinomials and difference of squares.
Blank Lesson
Lesson 2.6 Video
Homework 2.6 - Part 1 - Kuta Software
Homework 2.6 - Part 2 - Kuta Software
Lesson 2.7
In this lesson we explore what it means to solve a quadratic in preparation for the next unit - applications of factoring. We can conveniently use this skill to also find restrictions on a variable when simplifying rational expressions - Lessons 2.8 and 2.9.
Lesson 2.8
In this lesson we get an introductory to the idea of what a restriction is in an equation along with where they might be found. We will pull upon our solving skills from Lesson 2.7 in order to identify what values of x don’t exist.
Blank Lesson
Lesson 2.9
In this lesson we look at applying our factoring skills to simplifying rational expressions. Each piece of the expression is factored individually, values of x that make the denominator zero (lesson 2.8) are stated as restrictions, and then any factors that are appear in the numerator and the denominator can be divided out which ultimately simplifies the expression.
Blank Lesson
Lesson 2.9 (question f) Video
Here you can find a comprehensive review of the concepts covered in this unit.
Expansion and Area Questions
Scaffolded Factoring
Assorted Factoring
