7.5 Factoring Linear Expression

GCF Also known as: The Greatest Common Factor The largest number that can be divided into all

Finding the Greatest Common Factor Cake Method For example, Find the GCF of 28 and 36 Hmm…. What number can divide both 28 and 36? Hmm…. What number can divide both 14 and 18? Hmm…. What number can divide both 7 and 9? 28 36 2 Multiply all of the side numbers to find the GCF 14 18 2 1 7 9 The GCF is 4.

Finding the Greatest Common Factor Now let’s apply variables! For example, Find the GCF of 6ab and 4a 6ab 4a 2 Multiply all of the side numbers and variables to find the GCF 3ab 2a a 1 3b 2 The GCF is 2a.

Finding the Greatest Common Factor Let’s kick it up a notch! For example, Find the GCF of 3x2y and 4xy2 3x2y 4xy2 3x2y 3 • x • x • y x 3xy 4y2 4y2 4 • y • y y 1 3x 4y The GCF is xy.

Examples A) Find the GCF of 14c2 and 35c 2c2 2 • c • c 14c2 35c 7 2c2 The GCF is 7c.

Examples B) Find the GCF of 6a3b and 4a2b 3a3b 3 • a • a • a • b 2a2b 2 • a • a • b a 3a2b 2ab b 3ab 2b Once you get the hang of this method, you can start to factor out more than 1 variable, like a2 or a2b. 1 3a 2 2• a • a • b The GCF is 2a2b.

Factored Form ab+ac = a(b+c) To be in most simplest form the numbers inside the () can not have any common factors other then 1.

“Factoring Polynomials” the REVERSE of the Distributive Property 5(x + 3) = 5x + 15 “Factoring Polynomials” the REVERSE of the Distributive Property

Steps to Factor Find the GCF Write the GCF on the outside of the () Divide the GCF by all the terms and write the quotient inside the () Make sure that the terms in the () only have a GCF of 1

Ex 1:Factor: 10x + 15 + 3 2x Check your answer!!!!!

Ex 2 Factor: 12x + 4 3x + 1 Check your answer!!!!!

Example 3: Factor 4x +28 x 7 4 ( + )

Example 4: Factor 4x +35 Cannot be factored

Example 5: Factor 3 +33x 3 ( + ) 11x 1

Homework Page 319 (10-40) even