1 / 11

Factoring Polynomials

Factoring Polynomials. Thursday, March 6, 2014. Greatest Common Factor. No matter what type of polynomial you are factoring, you always factor out the GCF first!. What if it’s a binomial ?. 1 st – Factor out GCF 2 nd – Difference of Squares 3 rd – Sum of Cubes

raine
Download Presentation

Factoring Polynomials

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. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Factoring Polynomials Thursday, March 6, 2014

  2. Greatest Common Factor • No matter what type of polynomial you are factoring, you always factor out the GCF first!

  3. What if it’s a binomial? • 1st – Factor out GCF • 2nd – Difference of Squares • 3rd – Sum of Cubes • 4th – Difference of Cubes

  4. Binomials continued … • Difference of squares – Ex: (4x2 – 9)  (2x + 3) (2x – 3) • Sum of cubes – Ex: 8x3 + 27  (2x +3) (4x2 – 6x + 9) • Difference of cubes – Ex: x3 – 8  (x – 2) (x2 + 2x + 4)

  5. What if it’s a trinomial? • 1st – Factor out GCF • 2nd – Perfect Square Trinomial • 3rd – “Unfoil”

  6. Trinomials continued… • 1st term is a perfect square, last term is a perfect square, middle term is double the product of the square roots of the first and last terms. Then, subtract or add depending on sign of middle term. • Ex: 4x2 – 4x +1  (2x -1)2 Square root of 4x2 is 2x, square root of 1 is 1, 2(2x * 1) = 4x • Ex: 9x2 + 24x + 16  (3x + 4)2 Square root of 9x2 is 3x, square root of 16 is 4, 2(3x * 4) = 24x

  7. Trinomials continued… “Unfoil” • Find the factors of the first and last terms. How can we get the middle term with them? • If it’s a + and + or a – and +, you need to multiply and then add to get the middle term. You will factor as a - - or a + +. • If it’s a + and -, then you need to multiply then subtract to get the middle term. You will factor as a + -.

  8. Examples: • If it’s a + and + or a – and +, you need to multiply and then add to get the middle term. You will factor as a + + or a - -. • a2 + 7a + 6 = (a + 6) (a + 1) • x2 – 5x + 6 = (x – 3) (x – 2)

  9. Examples: • If it’s a + and -, then you need to multiply then subtract to get the middle term. You will factor as a + -. • x2 + 4x – 5 = (x + 5) (x – 1)

  10. What if it’s a polynomial of 4 or more? • 1st – Factor out GCF • 2nd – Factor by Grouping

  11. Factoring by Grouping Ex: x3 + 3x2 + 2x +6 • Group two terms together. (x3 + 3x2) + (2x + 6) 2. Factor out a GCF from each separate binomial to get a common binomial. x2 (x + 3) + 2(x + 3) 3. Factor out the common binomial. (x+3) (x2 + 2)

More Related