factoring polynomials
Download
Skip this Video
Download Presentation
Factoring Polynomials

Loading in 2 Seconds...

play fullscreen
1 / 20

Factoring Polynomials - PowerPoint PPT Presentation


  • 83 Views
  • Uploaded on

Factoring Polynomials. Algebra I. Vocabulary. Factors – The numbers used to find a product. Prime Number – A whole number greater than one and its only factors are 1 and itself. Composite Number – A whole number greater than one that has more than 2 factors. Vocabulary.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Factoring Polynomials' - reese


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
vocabulary
Vocabulary
  • Factors – The numbers used to find a product.
  • Prime Number – A whole number greater than one and its only factors are 1 and itself.
  • Composite Number – A whole number greater than one that has more than 2 factors.
vocabulary1
Vocabulary
  • Factored Form – A polynomial expressed as the product of prime numbers and variables.
  • Prime Factoring – Finding the prime factors of a term.
  • Greatest Common Factor (GCF) – The product of common prime factors.
prime or composite1
Prime or Composite?

Ex) 36

Composite.

Factors: 1,2,3,4,6,9,12,18,36

Ex) 23

Prime.

Factors: 1,23

prime factorization
Prime Factorization

Ex) 90 = 2 ∙ 45

= 2∙ 3∙ 15

= 2∙ 3 ∙ 3 ∙ 5

OR use a factor tree:

90

9 10

3 3 2 5

prime factorization of negative integers
Prime Factorization of Negative Integers

Ex) -140 = -1 ∙ 140

= -1 ∙ 2 ∙ 70

= -1 ∙ 2 ∙ 7 ∙ 10

= -1 ∙ 2 ∙ 7 ∙ 2 ∙ 5

now you try
Now you try…

Ex) 96

Ex) -24

now you try1
Now you try…

Ex) 96

2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 ∙ 3

Ex) -24

-1 ∙ 2 ∙ 2 ∙ 2 ∙ 3

prime factorization of a monomial
Prime Factorization of a Monomial

12a²b³= 2 · 2 · 3 · a · a · b · b · b

-66pq²= -1 · 2 · 3 · 11 · p · q · q

finding gcf
Finding GCF

Ex) 48 = 2 ∙ 2 ∙ 2 ∙ 2 ∙ 3

60 = 2 ∙ 2 ∙ 3 ∙ 5

GCF = 2 · 2 · 3 = 12

Ex) 15 = 3 · 5

16 = 2 · 2 · 2 · 2

GCF – none = 1

now you try2
Now you try…

Ex) 36x²y

54xy²z

now you try3
Now you try…

Ex) 36x²y = 2 · 2 · 3 · 3 · x · x · y

54xy²z = 2 · 3 · 3 · 3 · x · y · y · z

GCF = 18xy

factoring using the reverse distributive property
Factoring Using the (Reverse) Distributive Property
  • Factoring a polynomial means to find its completely factored form.
factoring using the reverse distributive property1
Factoring Using the (Reverse) Distributive Property
  • First step is to find the prime factors of each term.

Ex) 12a²+ 16a

12a²= 2 · 2 · 3 · a · a

16a = 2 · 2 · 2 · 2 · a

factoring using the reverse distributive property2
Factoring Using the (Reverse) Distributive Property
  • First step is to find the prime factors of each term.
  • Next step is to find the GCF of the terms in the polynomial.

Ex) 12a²+ 16a

12a²= 2 · 2 · 3 · a · a

16a = 2 · 2 · 2 · 2 · a

GCF = 4a

factoring using the reverse distributive property3
Factoring Using the (Reverse) Distributive Property
  • First step is to find the prime factors of each term.
  • Next step is to find the GCF of the terms in the polynomial.
  • Now write what is left of each term and leave in parenthesis.

Ex) 12a²+ 16a

12a²= 2 · 2 · 3 · a · a

16a = 2 · 2 · 2 · 2 · a

4a(3a + 4)

factoring using the reverse distributive property4
Factoring Using the (Reverse) Distributive Property
  • First step is to find the prime factors of each term.
  • Next step is to find the GCF of the terms in the polynomial.
  • Now write what is left of each term and leave in parenthesis.

Ex) 12a²+ 16a

12a²= 2 · 2 · 3 · a · a

16a = 2 · 2 · 2 · 2 · a

4a(3a + 4)

Final Answer 4a(3a + 4)

another example
Another Example:

18cd²+ 12c²d + 9cd

another example1
Another Example:

18cd²+ 12c²d + 9cd

18cd² = 2 · 3 · 3 · c · d · d

12c²d = 2 · 2 · 3 · c · c · d

9cd = 3 · 3 · c · d

GCF = 3cd

Answer: 3cd(6d + 4c + 3)

ad