Basic Factoring Review Students will be able to factor a quadratic with a leading coefficient of 1.

Basic Factoring Review

Basic Factoring Review Write the following equation: 𝒚= 𝒂 𝟐 −𝟔𝒂+𝟖

Basic Factoring Review STEP 1: 𝒚= 𝒂 𝟐 −𝟔𝒂+𝟖 Multiply the first term (𝑡ℎ𝑒 𝑠𝑞𝑢𝑎𝑟𝑒𝑑 𝑡𝑒𝑟𝑚) and last term (𝑡ℎ𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡) including their “signs” and place the product in the top of the diamond 𝟖 𝒂 𝟐

Basic Factoring Review STEP 2: 𝒚= 𝒂 𝟐 −𝟔𝒂+𝟖 Put the center term (𝑡ℎ𝑒 𝑓𝑖𝑟𝑠𝑡 𝑝𝑜𝑤𝑒𝑟 𝑡𝑒𝑟𝑚) in the bottom of the diamond. 𝟖 𝒂 𝟐 −𝟔𝒂

Basic Factoring Review STEP 3: 𝒚= 𝒂 𝟐 −𝟔𝒂+𝟖 Create a list of all the factors of the term in the top of the diamond. 𝟖𝒂∗𝟏𝒂 𝟒𝒂∗𝟐𝒂 𝟖 𝒂 𝟐 −𝟔𝒂

Basic Factoring Review STEP 4: 𝒚= 𝒂 𝟐 −𝟔𝒂+𝟖 Decide which of the factors you can combine to equal the term in the bottom of the diamond. 𝟖𝒂∗𝟏𝒂 𝟒𝒂∗𝟐𝒂 𝟖 𝒂 𝟐 −𝟔𝒂

Basic Factoring Review STEP 5: 𝒚= 𝒂 𝟐 −𝟔𝒂+𝟖 Decide which of the factors you can combine to equal the term in the bottom of the diamond. 𝟖𝒂∗𝟏𝒂 𝟒𝒂∗𝟐𝒂 𝟖 𝒂 𝟐 −𝟔𝒂

Basic Factoring Review STEP 5: 𝒚= 𝒂 𝟐 −𝟔𝒂+𝟖 Place those factors, one in each side of the diamond, so that their total equals the term in the bottom of the diamond. Adjust signs as needed. 𝟖 𝒂 𝟐 −𝟒𝒂 −𝟐𝒂 −𝟔𝒂

Basic Factoring Review STEP 6: 𝒚= 𝒂 𝟐 −𝟔𝒂+𝟖 Check that when you multiply the terms on the sides of the diamond, they equal the top, but when you combine them, they equal the bottom. 𝟖 𝒂 𝟐 −𝟒𝒂 −𝟐𝒂 −𝟔𝒂

Basic Factoring Review STEP 7: 𝒚= 𝒂 𝟐 −𝟔𝒂+𝟖 Place the terms as follows in the box. (Track the terms in the circles as they move in the box.) 𝟖 𝒂 𝟐 𝒂 𝟐 −𝟒𝒂 −𝟒𝒂 −𝟐𝒂 −𝟐𝒂 𝟖 −𝟔𝒂

Basic Factoring Review STEP 8: 𝒚= 𝒂 𝟐 −𝟔𝒂+𝟖 Fill out the cross products as you see here. Your cross products become your factors. 𝒂 −𝟒 𝒂 𝒂 𝟐 −𝟒𝒂 −𝟐 −𝟐𝒂 𝟖

Basic Factoring Review DONE! 𝒚= 𝒂 𝟐 −𝟔𝒂+𝟖 The factors of my equation are (𝒂−𝟒)(𝒂−𝟐)

Basic Factoring Review Now YOU try: 𝒚= 𝒏 𝟐 +𝟐𝒏−𝟖 My two factors will be: ( )( )

Basic Factoring Review Now YOU try: 𝒚= 𝒏 𝟐 +𝟐𝒏−𝟖 ( )( )