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

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

4.1.1 Introduction to Factoring Expressions

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

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

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

Homework Worksheet basic factoring

4.1.2 and 4.1.3 Factoring with Area Models and Factoring without

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

Examples

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

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

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

Example

Homework Worksheet

4.1.4 Factoring Completely

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

Example

Homework Pg 225 4-39

4.1.5 Factoring Special Cases

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

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

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

Homework Worksheet