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 II, Module 1, Lesson 13

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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