Magicians Factoring Expressions Greatest Common Factor GCF Difference

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) b) c) d) e) 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. a) b) c) d) e) f) x, x 2, x 3 xy, x 2 y 2 x 3, 8 x 2 3 x 3, 6 x 2 4 x 2, 5 y 3 x x 2 xy 2 x 2 3 x 2 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) b) c) d) e) 2 x + 4 y 5 a – 5 b 18 x – 6 y 2 m + 6 mn 5 x 2 y – 10 xy 2(x + 2 y) 5(a – b) How can you check? 6(3 x – y) 2 m(1 + 3 n) 5 xy(x - 2)

FACTORING by GCF Take out the GCF EX: 15 xy 2 – 10 x 3 y + 25 xy 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: 5 xy( 3 y – 2 x 2 + 5 y 2 )

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

Ex 1 2 • 15 x – 5 x • GCF = 5 x • 5 x(3 x - 1)

Ex 2 2 • 8 x –x • GCF = x • x(8 x - 1)

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

What is a Perfect Square • Any term you can take the square root evenly (No decimal) • 25 • 36 • 1 • 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: Solution: Take the square root of (x – 8)(x + 8) each part. One gets a + and one gets a -. Check answer by FOIL.

YOUR TURN!!

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

Example 2 2 • x – 16 • (x + 4)(x – 4)

Ex 3 2 • 36 x – 25 • (6 x + 5)(6 x – 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 • 2 b 2 x – 50 x • GCF = 2 x 2 • 2 x(b – 25) nd • 2 term is the diff of 2 squares • 2 x(b + 5)(b - 5)

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

Exit Slip • On a post it note write these 2 things: (with your name) • 1. Define what factors are? • 2. What did you learn today about factoring? • Put them on the bookshelf on the way out!