1. Factor the GCF out of each.
Teacher (Magnani)
Warm-Up 2.5
Factor the GCF out of each.
8x4 – 14x3 + 20x2 – 44x
9x3y + 18x4y2 – 3xy
= 2x(4x3 – 7x2 + 10x – 22)
= 3xy(3x2 + 6x3y – 1)

2. SSBAT factor a polynomial using grouping.
Algebra 3
Lesson 2.5
Objective:
SSBAT factor a polynomial using grouping.
Standards: M11.D.2.2.2

3. Factoring by Grouping
Use this method when you have 4 terms and you are able to split the polynomial into groups that contain a GCF within each group

4. Steps for Factoring by Grouping
Split the polynomial into 2 or more groups so that each group has a GCF.
Factor out the GCF of each group formed.
The expressions left behind in each should be identical (if not you can not factor the polynomial).
If so, the identical expression will be one parenthesis and the grouping of the GCFs will be the other parenthesis.

5. Examples: Factor each by grouping.
10xy + 14x + 15y + 21
= (10xy + 14x) + (15y + 21)
= 2x(5y + 7) + 3(5y + 7)
= (2x + 3)(5y + 7)

6. 4x3 + 5x2 – 24x – 30
= (4x3 + 5x2) + (-24x – 30)
= x2(4x + 5) – 6(4x + 5)
= (x2 – 6)(4x + 5)

7. 3. 4m4 – 16m3 + m – 4
= (4m4 – 16m3) + (m – 4)
= 4m3(m – 4) + 1(m – 4)
= (4m3 + 1)(m – 4)

8. Teacher (Magnani)
4. 8x z + 3xz
= (8x + 48) + (18z + 3xz)
= 8(x + 6) + 3z(6 + x)
= 8(x + 6) + 3z(x + 6)
= (8 + 3z)(x + 6)

9. a2 – 12ac – 21ab + 14bc
= (18a2 – 12ac) + (-21ab + 14bc)
= 6a(3a – 2c) – 7b(3a – 2c)
= (6a – 7b)(3a – 2c)

10. xy – 20x + 3y – 21
= (4xy – 20x) + (3y – 21)
= 4x(y – 5) + 3(y – 7)
Can not be factored. Prime.

11. On Your Own.
Factor by Grouping.
9mn – 6n + 12m – 8
= (3m – 2)(3n + 4)

12. Homework
Worksheet 2.5