Mastering Factoring

Mastering Factoring

Student Outcomes

• Students will use the structure of polynomials to identify factors.

New York State Common Core Math Algebra II, Module 1, Lesson 13

Worksheets for Algebra 2

Classwork

Opening Exercises

Factor each of the following expressions. What similarities do you notice between the examples in the left column and those on the right?
a. 𝑥² −1
b. 9𝑥² −1
c. 𝑥² + 8𝑥 + 15
d. 4𝑥² + 16𝑥 + 15
e. 𝑥² − 𝑦²
f. 𝑥⁴ − 𝑦⁴

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Example 2

Factor 4𝑥²𝑦⁴ − 25𝑥⁴𝑧⁶.

Exercise 1

1. Factor the following expressions:
   a. 4𝑥² + 4𝑥 − 63
   b. 12𝑦² −24𝑦 − 15

Exercises 2–4

Factor each of the following, and show that the factored form is equivalent to the original expression.
2. 𝑎³ + 27
3. 𝑥³ − 64
4. 2𝑥³ + 128

Lesson Summary
In this lesson we learned additional strategies for factoring polynomials.

• The difference of squares identity 𝑎2 −𝑏2 = (𝑎 − 𝑏)(𝑎 + 𝑏) can be used to factor more advanced binomials.
• Trinomials can often be factored by looking for structure and then applying our previous factoring methods.
• Sums and differences of cubes can be factored by the formulas
  𝑥³ + 𝑎³ = (𝑥 + 𝑎)(𝑥² − 𝑎𝑥 − 𝑎²)
  𝑥³ − 𝑎³ = (𝑥 − 𝑎)(𝑥² + 𝑎𝑥 + 𝑎²)

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