Lesson 5.4 Other Factoring Strategies

Lesson 5.4 video link here. (Video under development)
Some polynomials can be factored using different methods than those you've seen thus far. This lesson explores two types of polynomials that can be factored using special strategies.


In Lesson 5.4, you will learn about

  • factoring a difference of squares

  • factoring a perfect square trinomial

 

Warm Up

 

Investigation

When subtracting the areas of two squares, some interesting patterns can be seen.

If you are unable to access this applet, skip ahead to the Alternate Investigation.

Difference of Squares

30 January 2014, Created with GeoGebra

  1. In the applet, the larger square has a side length of 10. The smaller square has side length a, which can be adjusted. Try adjusting the a-value. Explain how this pair of squares represents the subtraction of two areas.

  2. What area value must the blue and brown sections of the diagram always add to? Turn on "show values" to check your prediction.

  3. Once the blue area has been subtracted from the brown square, the remaining brown portions can always be rearranged into a rectangle. Explain why this is true. Turn on "show rearranged rectangles" to check your explanation.

  4. The brown area minus the blue area can be represented as . Use the first diagram to explain why this is true.

  5. How can you use the a-value to determine the length, l, and width, w, of the rectangle formed in the second diagram?

  6. Use the expressions for the length and width of the new rectangle to factor .

 

Alternate Investigation

If you are unable to access Difference of Squares, complete Investigate Factoring
Differences of Squares on pp. 238 - 239 of Mathematics 10.