1. Chapter 4 Factoring
Students will develop a method to change a quadratic expression written as a sum into its product form, also called its factored form. Then they will identify patters for factoring quadratics expressions

2. Factoring
Basic idea is to undo a multiplication Break something down into 2 polynomials that multiply into it We will talk about basic factoring and factoring polynomials

3. 4.1.1 Introduction to Factoring Expressions

4. Introduction
Terms Number, variable or combination of both separated by + or – Polynomial Combination of terms separated by + and – Monomial One term Binomial two terms Trinomial 3 terms (quadratics) Degree Highest exponent in the problem Leading coefficient When terms are put in order of exponents, highest to lowest, the coefficient of the first term

5. Review of multiplying Polynomails
Box method FOIL method Area model using algebra Tiles Using your algebra Tiles go through 4-1 Multiple types of tiles use sheet in bag to help set up the picture for 4-1 Dimensions of the picture you would multiple to get area, dimensions are the factored form

6. 4-2 Using algebra tiles
Work through exercise 4-2 and come up with a design that might fit the situation What would be the dimensions

7. Homework
Worksheet basic factoring

8. 4.1.2 and 4.1.3 Factoring with Area Models and Factoring without

9. Factoring binomials
Think of the terms and made up of numbers and letter and treat them differently
What is the largest number both coefficients can be divided by
Look at common variables, what is the lowest exponent
Repeat step 2 as needed
Answers from step 1 and 2 write outside a set of ( )
Divide original terms by what you wrote outside and write remaining values inside

10. Examples

11. Factoring Trinomials with leading coefficient of 1
a is leading coefficient
b is second term coefficient
c is third term or constant
Find factors of c that add to b
(x one factor)(x second factor)
+ or – sign is the sign of the factor

12. Examples
Factors of numbers are two numbers that multiple together and give you the original Depending on original number factors can be positive, negative or both

13. Factoring when a is not 1 Put in order Multiply a and c
Find factors that add to b
Rewrite the trinomial using the factors, always a plus between
Break apart the b term using the 2 factors, make sure you still have the x, I always put the negative first if I have one
Group first 2 terms in ( ) and last two terms in ( )
Factor first set of ( ) and factor second set of ( ), what is inside the ( ) should be the same
Group what is outside the ( ) into a binomial and put into a set of ( ), write the repeated ( ) next to it

14. Example

15. Homework
Worksheet

16. 4.1.4 Factoring Completely

17. Factoring completely This just adds one extra step
Is there something that can be factored out of all terms before you start factoring the trinomial
Is there a number everything can be divided by
Is there a variable everything can be divided by

18. Example

19. Homework Pg

20. 4.1.5 Factoring Special Cases

21. 4-45 Special quadratics
Factor the following and see if you notice a pattern Try to come up with a rule for each

22. Perfect Square
When you factor this polynomial you get both binomials the same
A little short cut
Is first term a perfect square
Is third term a perfect square
Is second term equal to 2 times square root of first times square root of 3rd
If yes to all three then you can just fill in the blanks

23. Difference of two square
When you factored these you should notice that the factored binomials are the same except one is plus and one is minus
Again a little shortcut
Are there only 2 terms
Is first term a perfect square
Is second term a perfect square
Is there a minus between
If yes to all about just fill in the blanks

24. Homework
Worksheet