magicians factoring expressions -greatest common factor (gcf) -difference of 2 squares

Magicians

They are all MASTERS of Magic!!

It is my GOAL

for each of you to become

MASTERS of

FACTORING

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 1st before any other method

• Divide Out the Biggest common number/variable from each of the terms

Greatest Common Factorsaka 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, 8

2

-56

161

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, x2

b) x2, x3

c) xy, x2y

d) 2x3, 8x2

e) 3x3, 6x2

f) 4x2, 5y3

xx2

xy

2x2

Greatest Common Factorsaka GCF’s

3x2

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) 5x2y – 10xy

2(x + 2y)

6(3x – y)

5(a – b)

5xy(x - 2)

2m(1 + 3n)

Greatest Common Factorsaka GCF’s

How can you check?

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)

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

5

6

1

x2y

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!!

Using White Boards

Example 1

•(9x2 – 16)

•(3x + 4)(3x – 4)

Example 2

•x2 – 16

•(x + 4)(x –4)

Ex 3

•36x2 – 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

• 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