Magicians

Factoring Expressions -Greatest Common Factor (GCF) -Difference of 2 Squares

Objectives I can factor expressions using the Greatest Common Factor Method (GCF) I can factor expressions using the Difference of 2 Squares Method

What is Factoring? Quick Write: Write down everything you know about Factoring from Algebra-1 and Geometry? You can use Bullets or give examples 2 Minutes Share with partner!

Factoring? Factoring is a method to find the basic numbers and variables that made up a product. (Factor) x (Factor) = Product Some numbers are Prime, meaning they are only divisible by themselves and 1

Method 1 Greatest Common Factor (GCF) – the greatest factor shared by two or more numbers, monomials, or polynomials ALWAYS try this factoring method 1 st before any other method Divide Out the Biggest common number/variable from each of the terms

Greatest Common Factors aka GCF’s Find the GCF for each set of following numbers. Find means tell what the terms have in common. Hint: list the factors and find the greatest match. a)2, 6 b)-25, -40 c)6, 18 d)16, 32 e)3, No common factors? GCF =1

Find the GCF for each set of following numbers. Hint: list the factors and find the greatest match. a)x, x 2 b)x 2, x 3 c)xy, x 2 y d)2x 3, 8x 2 e)3x 3, 6x 2 f)4x 2, 5y 3 x x2x2 xy 2x 2 Greatest Common Factors aka GCF’s 3x 2 1 No common factors? GCF =1

Factor out the GCF for each polynomial: Factor out means you need the GCF times the remaining parts. a)2x + 4y b)5a – 5b c)18x – 6y d)2m + 6mn e)5x 2 y – 10xy 2(x + 2y) 6(3x – y) 5(a – b) 5xy(x - 2) 2m(1 + 3n) Greatest Common Factors aka GCF’s How can you check?

FACTORING by GCF Take out the GCFEX: 15xy 2 – 10x 3 y + 25xy 3 How: Find what is in common in each term and put in front. See what is left over. Check answer by distributing out. Solution: 5xy( )3y – 2x 2 + 5y 2

FACTORING Take out the GCFEX: 2x 4 – 8x 3 + 4x 2 – 6x How: Find what is in common in each term and put in front. See what is left over. Check answer by distributing out. Solution: 2x (x 3 – 4x 2 + 2x – 3)

Ex 1 15x 2 – 5x GCF = 5x 5x(3x - 1)

Ex 2 8x 2 – x GCF = x x(8x - 1)

Ex 3 8x 2 y 4 + 2x 3 y x 4 y 3 GCX = 2x 2 y 3 2x 2 y 3 (4y + xy 2 – 6x 2 )

Method #2 Difference of Two Squares a 2 – b 2 = (a + b)(a - b)

What is a Perfect Square Any term you can take the square root evenly (No decimal) x 2 y 4

Difference of Perfect Squares x 2 – 4= the answer will look like this: ( )( ) take the square root of each part: ( x 2)(x 2) Make 1 a plus and 1 a minus: (x + 2)(x - 2 )

FACTORING Difference of Perfect Squares EX: x 2 – 64 How: Take the square root of each part. One gets a + and one gets a -. Check answer by FOIL. Solution: (x – 8)(x + 8)

YOUR TURN!!

Example 1 (9x 2 – 16) (3x + 4)(3x – 4)

Example 2 x 2 – 16 (x + 4)(x –4)

Ex 3 36x 2 – 25 (6x + 5)(6x – 5)

More than ONE Method It is very possible to use more than one factoring method in a problem Remember: ALWAYS use GCF first

Example 1 2b 2 x – 50x GCF = 2x 2x(b 2 – 25) 2 nd term is the diff of 2 squares 2x(b + 5)(b - 5)

Example 2 32x 3 – 2x GCF = 2x 2x(16x 2 – 1) 2 nd term is the diff of 2 squares 2x(4x + 1)(4x - 1)

Exit Slip On the back of your Yellow Sheet write these 2 things: 1. Define what factors are? 2. What did you learn today that was not on the front of your yellow sheet? Put them in Basket on way out!

Homework WS 5-1