1. Factoring by Grouping

2. When you have 4 terms
Remember– To factor out a GCF, we write the GCF on the outside and divide each term by the GCF.
Ex) x5y – x3y + 3y = y(x5 – x3 + 3)
You try: 3x2y - 9xy + 18xy2
3xy(x – 3 + 6y)

3. So, if instead of a variable, our GCF is a binomial, we do the same thing:
3(x – 2) + 5y(x – 2)
Our GCF is: (x – 2)
When we pull that out we get…
(x – 2) (3 + 5y)

4. You try: x(a – 4) – 3( a – 4) Did you get: (a - 4)(x - 3)???
m(p + 3) + q(p + 3)
Did you get: (p + 3)(m + q)???

5. What if the GCF is not obvious?
What if I have a problems like:
x2 + 3x + 2xy + 6y
That is when we have to group terms together. Always try to group the 1st 2 and the last 2.
x(x + 3) + 2y(x + 3)
(x + 3)(x + 2y)
Take out the GCF of each group
What is in parentheses will be the same (most of the time)

6. Let’s try: y2 – 5wy + 4y - 20w y (y – 5w) + 4(y – 5w) (y – 5w)(y + 4)
2) ab + 7b – 3a – 21
b(a + 7) – 3(a + 7)
(a + 7)(b – 3)
If the middle sign is a negative, you must remove a negative from the second set. Remember, when you divide a number by a negative, the sign changes

7. What if what is in my parentheses is not the same???
x2 – 5x3 + 15x – 3
x2(1 – 5x) + 3(5x – 1)
x2(1 – 5x) - 3(1 – 5x)
(1 – 5x)(x2 – 3)
You try: ax - bx + by – ay
x(a - b) + y (b - a)
x(a - b) – y (a – b)
(a – b) (x – y)
Is -1(5x – 1) the same thing as (1 -5x)????
Yes!!!! So, change that +3 to
a -3 and then the insides of
the ( ) will be the same thing!!

8. Try these: 1. 5xy2 – 20x + 3y3 – 12y 2x3 + 10x – x2y - 5y
12n3 + 15n2 + 4n + 5
Answers: 1. (5x + 3y)(y2 – 4)
(5x + 3y)(y + 2)(y – 2)
2. (2x – y)(x2 + 5) 3. (3n2 + 1)(4n + 5)

9. Homework 1. 2x3 + 4x2 + x + 2 2. 2x3 + 6x2 + 3x + 9