Magicians

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

I can factor expressions using the Greatest Common Factor Method (GCF) 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 1st 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. 2, 6 -25, -40 6, 18 16, 32 3, 8 2 -5 6 16 1 No common factors? GCF =1

Greatest Common Factors aka GCF’s Find the GCF for each set of following numbers. Hint: list the factors and find the greatest match. x, x2 x2, x3 xy, x2y 2x3, 8x2 3x3, 6x2 4x2, 5y3 x x2 xy 2x2 3x2 1 No common factors? GCF =1

Greatest Common Factors aka GCF’s Factor out the GCF for each polynomial: Factor out means you need the GCF times the remaining parts. a) 2x + 4y 5a – 5b 18x – 6y 2m + 6mn 5x2y – 10xy 2(x + 2y) How can you check? 5(a – b) 6(3x – y) 2m(1 + 3n) 5xy(x - 2)

FACTORING by GCF Take out the GCF EX: 15xy2 – 10x3y + 25xy3 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 – 2x2 + 5y2

FACTORING Take out the GCF EX: 2x4 – 8x3 + 4x2 – 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 (x3 – 4x2 + 2x – 3)

Ex 1 15x2 – 5x GCF = 5x 5x(3x - 1)

Ex 2 8x2 – x GCF = x x(8x - 1)

Ex 3 8x2y4+ 2x3y5 - 12x4y3 GCX = 2x2y3 2x2y3 (4y + xy2 – 6x2)

Difference of Two Squares a2 – b2 = (a + b)(a - b) Method #2 Difference of Two Squares a2 – b2 = (a + b)(a - b)

What is a Perfect Square Any term you can take the square root evenly (No decimal) 25 36 1 x2 y4

Difference of Perfect Squares x2 – 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: x2 – 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 (9x2 – 16) (3x + 4)(3x – 4)

Example 2 x2 – 16 (x + 4)(x –4)

Ex 3 36x2 – 25 (6x + 5)(6x – 5)

ALWAYS use GCF first 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 2b2x – 50x GCF = 2x 2x(b2 – 25) 2nd term is the diff of 2 squares 2x(b + 5)(b - 5)

Example 2 32x3 – 2x GCF = 2x 2x(16x2 – 1) 2nd 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