Mastering Factoring


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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

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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