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

2. Basic Factoring Review

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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

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

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

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