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9.6: Factoring Special Products

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Learning Objectives

At the end of this lesson, students will be able to:

  • Factor the difference of two squares.
  • Factor perfect square trinomials.
  • Solve quadratic polynomial equation by factoring.

Vocabulary

Terms introduced in this lesson:

recognizing special product
factoring perfect square trinomials
quadratic polynomial equations
double root

Teaching Strategies and Tips

Emphasize that students are reversing the special-products formulas introduced three lessons ago.

Have students use the vocabulary:

  • a^2 - b^2 is a difference of squares.
  • (a + b)(a - b) is the product of a sum and difference.
  • a^2 + 2ab + b^2 and a^2 - 2ab + b^2 are perfect square trinomials.
  • (a + b)^2 and (a - b)^2 are squares of binomials.

The key to factoring special products is recognizing the special form, but also determining what a and b are.

  • Recognizing perfect integer squares, for example, may be difficult to some students. Suggest that students break numbers down into prime factorization first. See Example 2.

Remind students to pull out -1 and/or the GCF in a polynomial before attempting to factor it. This simplifies the task dramatically.

Error Troubleshooting

General Tip: Remind students to check their solutions by substituting each in the original equation.

Review Question 8 is quadratic-like. Show students that x^4 = (x^2)^2.

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