Method 1: Generic Rectangle Once all of the areas are labeled, we have to find the dimensions. Factoring When given an expression with 3 terms, there are 2 methods of factoring that can be used. Remember that factoring is working backwards to write a multiplication problem. ** Because it is a multiplication problem, it does not matter which factor is the base and which is the height. Multiply base and height to find the area. x x + 5 Don’t forget to combine like terms! Use each of the factors for either the base or the height. Solutions: Once you have completed all the problems, click the mouse again for the solutions!Įxample 2 Again we are going to use the concept of area to multiply our 2 factors. The factored form: 4x(x+2)ħ Practice Use the concept of area to find the factored form of each of the following expressions. This height is the GREATEST COMMON FACTOR! 2) Use that height and the areas to find the base. When finding the dimensions you want to find the largest height possible. 4x 1) Find a height that works for both small rectangles. When asked to factor, you are given the area and are asked to find the dimensions. Think about the algebra tiles– can we build a rectangle? 4 Simplify the base! 2x Area = (base)(height) 8x + 12 = (2x + 3)(4) ** Don’t forget that using generic rectangles can save time!Ħ Factoring Example 2: Using Generic Rectangles x + 2 How can we work backwards from this process? x x Let’s look at the dimensions of the rectangle we made. 2x + 3 4 8x 12 A = bh The total area of the large rectangle is 8x + 12.ĥ Factoring We need to start with our solution: Distributive Property Area and Rectangles Multiply the inside terms by the outside value. AreaRectangle = (base)(height)Įxample 1: There are 2 methods used to multiply these expressions. Because factoring is the process of “undoing” multiplication, let’s review our multiplication techniques. All of our factoring methods are built around the idea of area of a rectangle.

There are several different methods used to factor algebraic expressions, or expressions that contain variables. Factoring “undoes” multiplication We can write numbers in terms of factors: What are the factors of 12? To factor 12, we would write it as a product of its factors: What is special about prime factors? These are special factors of 12 known as prime factors. Factoring is the process of writing an expression as a multiplication problem.

Factoring expressions