1 / 5

Factoring Special Case Polynomials Two terms :

Factoring Special Case Polynomials Two terms : Is it a difference of squares ? Factor by using: a 2 -b 2 = ( a+b )(a-b) Example 1: 36x 2 – 49 = (6x) 2 – 7 2 = (6x-7)(6x+7) Example 2: Factor  9 x 6  –  y 8

simone
Download Presentation

Factoring Special Case Polynomials Two terms :

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 Special Case Polynomials Two terms: Is it a difference of squares? Factor by using: a2-b2 = (a+b)(a-b) Example 1: 36x2 – 49 = (6x)2 – 72 = (6x-7)(6x+7) Example 2: Factor 9x6 – y8 Since 6 and 8 are bothevenexponents, and 9 is a perfectsquare, this can be rewritten as 9x6 – y8 = (3x3)2 – (y4)2 = (3x3 – y4)(3x3 + y4) Is it a difference of cubes? Factor by using a3 – b3 = (a - b)(a2 + ab+ b2) Is it a sum of cubes? Factor by using a3+ b3 = (a + b)(a2 - ab+ b2) Example: Factor 8x3 - 27 If the polynomial can’t be factored, it is PRIME. Three terms: Is it a perfect square trinomial? If it is it would be in the form a2x2 + 2abx + b2, which is factored as (a+b)2 or a2x2 + 2abx + b2which is factored as (a-b)2 Example: 4x2+ 12x + 9 = (2x)2 + 2(2)(3)x + 32 = (2x + 3)2 8x = (2x)3 27 = 33 (2x)3 - 32 = (2x – 3)((2x)2 + (2x)(3) + (3)2) = (2x – 3)(4x2 + 6x + 9)

  2. a •c Setting up the snowflake for… ax2 + bx + c ax ax b Fill the missing spaces of the snowflake with the two numbers that when multiplied give you “a • c” and when added together give you “b.” AIM: Understanding how to factor quadratic functions when a > 1 The SNOWFLAKE METHOD Let’s use the snowflake method to factor 3x2 + 8x +5 Step 1: Set up your snowflake. • Step 2: Fill in the missing spaces. • Step 3: Reduce the fractions on either side of • the snowflake and put in proper form. 3*5 = 15 1 3x 3x 5 3 1 8 ANSWER: ( 3x + 5)(x + 1)

  3. Use the snowflake method to factor 4x2 + 14x + 12 Snowflake method will not work if you don’t factor out the GCF! **Step 0: Take out a factor of 2! 2(2x2 + 7x + 6) Step 1: Set up your snowflake. Step 2: Fill in the missing spaces. Step 3: Reduce the fractions on either side of the snowflake and put in proper form. 2*6 = 12 1 2x 2x 4 3 2 7 Don’t forget the GCF in the answer! ANSWER: 2( x + 2)(2x + 3)

  4. Use the snowflake method to factor u4 – 3u2 - 4 This polynomial is a trinomial but is not of degree 2. However, since the degree(highest power) is even, then We can use substitution and make it a polynomial if degree 2. Letx = u2, then x2 = u4 Our substituted polynomial becomes x2 - 3x - 4 Step 1: Set up your snowflake. Step 2: Fill in the missing spaces. Step 3: Reduce the fractions on either side of the snowflake and put in proper form. Step 4: Don’t forget to put your original variable back in your factorization and factor more if necessary! • Can any of these • be factored more? (x – 4)(x +1) -4 • Now remember what x is: • (u2 – 4)(u2 + 1) -4 1 -3 Yes. Answer:(u + 2)(u -2)(u2 +1)

More Related