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Study Guides > Intermediate Algebra

Introduction: Special Cases

Why learn how to factor special cases?

Repeated pattern of interlocking plus signs, each row a different color following the rainbow spectrum. Some people like to find patterns in the world around them, like a game.  There are some polynomials that, when factored, follow a specific pattern. These include: Perfect square trinomials of the form: a2+2ab+b2{a}^{2}+2ab+{b}^{2} A difference of squares: a2b2{a}^{2}-{b}^{2} A sum of cubes: a3+b3{a}^{3}+{b}^{3} A difference of cubes: a3b3{a}^{3}-{b}^{3} In this lesson you will see you can factor each of these types of polynomials following a specific pattern.  You will also learn how to factor polynomials that have negative or fractional exponents. In this lesson you will learn how to do the following:
  • Recognize a polynomial that factors into a special product
  • Factor special products
  • Factor polynomials with negative or fractional exponents
  • Factor by substitution

The learning activities for this outcome include:

  • Read: Special Cases - Squares
  • Self-Check: Special Cases - Squares
  • Read: Special Cases - Cubes
  • Self-Check: Special Cases - Cubes
  • Read: More Factoring Methods
  • Self-Check: More Factoring Methods

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