Section 7.7: Factoring Applications

This section demonstrates how factoring can be used to solve real-world problems and equations efficiently.

Example 1: Solve Quadratic Equation

Solve: \( x^2 - 5x + 6 = 0 \)

Factor: \( x^2 - 5x + 6 = (x-2)(x-3) \)

Set each factor to 0: \( x-2=0 \Rightarrow x=2 \), \( x-3=0 \Rightarrow x=3 \)

Solution: \( x=2 \) or \( x=3 \)

Example 2: Area Problem

The area of a rectangle is \( x^2 + 5x + 6 \). Find its dimensions if length and width are integers.

Factor the quadratic: \( x^2 + 5x + 6 = (x+2)(x+3) \)

Possible dimensions: \( x+2 \) and \( x+3 \)

Practice Problems

  1. Solve: \( x^2 - 7x + 12 = 0 \)
  2. Solve: \( x^2 + 8x + 15 = 0 \)
  3. A rectangle has area \( x^2 + 9x + 14 \). Factor to find dimensions.
  4. Solve: \( x^2 - 2x - 8 = 0 \)
  5. Word problem: Product of two consecutive integers is 56. Find the integers.
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