1 / 12

§8.8 Factoring by Grouping

§8.8 Factoring by Grouping. Check: 6 x 3 + 3 x 2 – 4 x – 2 (2 x + 1)(3 x 2 – 2). = 6 x 3 – 4 x + 3 x 2 – 2 Use FOIL. = 6 x 3 + 3 x 2 – 4 x – 2 Write in standard form. Example 1: Factoring a Cubic Polynomial. Factor 6 x 3 + 3 x 2 – 4 x – 2.

pancho
Download Presentation

§8.8 Factoring by Grouping

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. §8.8 Factoring by Grouping

  2. Check: 6x3 + 3x2 – 4x – 2 (2x + 1)(3x2 – 2) = 6x3 – 4x + 3x2 – 2 Use FOIL. = 6x3 + 3x2 – 4x – 2 Write in standard form. Example 1: Factoring a Cubic Polynomial Factor 6x3 + 3x2 – 4x – 2. 6x3 + 3x2 – 4x – 2 = 3x2(2x + 1) – 2(2x + 1) Factor the GCF from each group of two terms. = (2x + 1)(3x2 – 2) Factor out (2x + 1).

  3. Example 2: Factoring a Polynomial Completely Factor 8t4 + 12t3 + 16t + 24. 8t4 + 12t3 + 16t + 24 = 4(2t4 + 3t3 + 4t + 6) Factor out the GCF, 4. = 4[t3(2t + 3) + 2(2t + 3)] Factor by grouping. = 4(2t + 3)(t3 + 2) Rewrite factors as two binomials.

  4. Find two factors of ac that have a sum b. Use mental math to determine a good place to start. Step 3:Factors Sum –2(18) = –36 –2 + 18 = 16 –3(12) = –36 –3 + 12 = 9 –4(9) = –36 –4 + 9 = 5 Example Ω: Factoring a Trinomial by Grouping Factor 24h2 + 10h – 6. Step 1:24h2 + 10h – 6 = 2(12h2 + 5h – 3)   Factor out the GCF, 2. Step 2: 12 • –3 = –36 Find the product of ac.

  5. Example Ω: Factoring a Trinomial by Grouping Step 4:12h2– 4h+ 9h – 3 Rewrite the trinomial. Step 5:4h(3h– 1) + 3(3h – 1) Factor by grouping. (4h + 3)(3h – 1) Rewrite factors as two binomials. 24h2 + 10h – 6 = 2(4h + 3)(3h – 1)Include the GCF in your final answer.

  6. Example 3: Finding the Dimensions of a Rectangular Prism A rectangular prism has a volume of 36x3 + 51x2 + 18x. Factor to find the possible expressions for the length, width, and height of the prism. Factor 36x3 + 51x2 + 18x. Step 1: 3x(12x2 + 17x + 6) Factor out the GCF, 3x. Step 2: 12 • 6 = 72 Find the product of ac.

  7. Find two factors of ac that have sum b. Use mental math to determine a good place to start. Step 3:Factors  Sum 4 • 18 4 + 18 = 22 6 • 12 6 + 12 = 18 8 • 9 8 + 9 = 17 Example 3: Finding the Dimensions of a Rectangular Prism A rectangular prism has a volume of 36x3 + 51x2 + 18x. Factor to find the possible expressions for the length, width, and height of the prism. Factor 36x3 + 51x2 + 18x.

  8. Example 3: Finding the Dimensions of a Rectangular Prism Step 4: 3x(12x2 + 8x + 9x + 6) Rewrite the trinomial. Step 5: 3x[4x(3x + 2) + 3(3x + 2)] Factor by grouping. 3x(4x + 3)(3x + 2) Rewrite the factors as binomials. The possible dimensions of the prism are: 3x, (4x + 3), and (3x + 2).

  9. Summary of Factoring: Factoring Polynomials 1.) Factor out the greatest common factor (GCF). 2.) If the polynomial has two terms or three terms, look for a difference of two squares, a product of two squares, or a pair of binomial factors. 3.) If there are four or more terms, group terms and factor to find common binomial factors. 4.) As a final check, make sure there are no common factors other than 1. Summary

  10. Assignment: Pg. 531-532 9-33 Left

More Related