1 / 5

Factoring Trinomials: Grouping Method Example

Learn to factor trinomials of the form ax^2 + bx + c using the grouping method. Follow steps to factor by grouping and see examples for better understanding.

carlosdennis
Download Presentation

Factoring Trinomials: Grouping Method Example

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 Trinomials of the Form ax2 + bx + c by Grouping 4.4

  2. Factoring by Grouping An alternative method that can be used to factor trinomials of the form ax2 + bx + c, a ≠ 1 is called the grouping method. This method uses factoring by grouping. Example • Factor xy + y + 2x + 2 by grouping. Notice that, although 1 is the GCF for all four terms of the polynomial, the first 2 terms have a GCF of y and the last 2 terms have a GCF of 2. xy + y + 2x + 2 = x·y + 1 ·y + 2·x + 2· 1 = y(x + 1)+ 2(x + 1)= (x + 1)(y + 2)

  3. Factoring by Grouping To Factor Trinomials by Grouping Step 1: Factor out a greatest common factor, if there is one other than 1. Step 2: For the resulting trinomial ax2 + bx + c, find two numbers whose product is a • c and whose sum is b. Step 3: Write the middle term, bx, using the factors found in Step 2. Step 4: Factor by grouping.

  4. Factoring by Grouping Example Factor each of the following polynomials by grouping. • x3 + 4x + x2 + 4 = x ·x2 + x· 4 + 1· x2 + 1· 4 = x(x2 + 4) + 1(x2 + 4) = (x2 + 4)(x + 1) • 2x3 – x2 – 10x + 5 = x2 · 2x – x2· 1 – 5· 2x – 5· (– 1) = x2(2x – 1) – 5(2x – 1) = (2x – 1)(x2 – 5)

  5. Factoring by Grouping Example Factor 2x – 9y + 18 – xy by grouping. Neither pair has a common factor (other than 1). So, rearrange the order of the factors. 2x + 18 – 9y – xy = 2 · x + 2· 9 – 9 · y – x· y = 2(x + 9) – y(9 + x) = 2(x + 9) – y(x + 9)Make sure the factors are identical. = (x + 9)(2 – y)

More Related