Factoring: The Greatest Common Factor Lesson

Factoring: The Greatest Common Factor Lesson

THE DISTRIVUTIVE PROPERTY

Review

Examples

• Multiply each term inside ( ) by the term in outside

• Simplify

More Examples

• Make sure to check the signs when outside term is negative

• The signs of the terms inside ( ) will change

Multiple Choice

Simplify the following expression using the distributive property.

9(−5x+8)

• 45x-72

• 45x+72

  
  

• -45x+72

• -45x-72

Multiple Choice

Which of the following represents the correct use of the distributive property for ....

 $3\left(x^2\ +\ 2x\ +\ 5\right)$  

•  $3\cdot x^2+2\cdot2x\ +3\cdot5$  

•  $3\cdot x^2+2x+5$  

•  $3x^2+5x+8$  

Multiple Choice

Simplify

 $-3\left(8x^2-7x+6\right)$  

•  $24x^2-21x-18$  

•  $-24x^2+21x+18$  

•  $24x^2+21x-18$  

•  $-24x^2+21x-18$  

Reversing the Distributive Property

Facctoring out the GCF

What are factors?

Factors are multiplied to produce a larger value or expression.

Factor tree

A factor tree show the prime numbers that are multiplied to create a specific value.

Prime numbers...1,2,3,5,7,11,13,19,23,..

Finding the GCF between two numbers

To find the GCF of two numbers: List the prime factors of each number. Multiply those factors both numbers have in common.

Multiple Choice

Find the Greatest Common Factor (GCF) of 28 and 40

• 4

• 2

• 8

• 7

Multiple Choice

Find the GCF between 45 and 15

• 3

• 5

• 10

• 15

Multiple Choice

Find the greatest common factor of 72 and 54

• 5

• 8

• 9

• 13

GCF with exponents

The term with the smallest power is the GCF

What does it mean "to factor" or to express in a factored form?

Show values or terms that have been multiplied to create a given value or expression.

Factoring out the Greatest Common Factor or GCF

• 1.  Identify the Greatest Common Factor (GCF) for each term.

• 2.  Divide each term by the GCF.

• 3.  Write the factored form: GCF(Remaining Terms)

• The GCF for the example to the right is

   $2y^2$  

Alternate method

Write each term in expanded form to identify the GCF. The remaining terms are are multiplied and will be inside the ( ) with the GCF outside.

Factoring GCF Video Link...copy and paste in search bar

https://www.youtube.com/watch?v=Y1Vd5wb0rnM

Fill in the Blanks

is the Greatest Common Factor for the expression

5k³ + 7k² + k

Multiple Choice

Factor 16x² + 18x + 12

• 4(4x² + 6x + 3)

• 2(8x² + 9x + 6)

• 2x(8x + 9 + 3)

• x(16x + 18 + 12)

Multiple Choice

Find the complete factored form of 4x³ + 2x² – 6x.

• 4x (x² + x – 3)

• 2x (2x² + x – 3)

• 2x (2x² + x – 6)

• x (4x² + 2x – 3)

Multiple Choice

What is the Greatest Common Factor for the terms in the expression...

 $12x^2-27x$  

• x

• 3

• 3x

• 9x

Multiple Choice

Write  $2n^2-8n^3$  in its factored form.

•  $2n^2\left(n-4n^2\right)$  

•  $2n^2\left(1-4n\right)$  

•  $3n\left(1-4n\right)$  

•  $2n^3\left(10-8n^2\right)$