Slide 1
Factoring Polynomials
Grouping, Trinomials, Binomials, GCF & Solving Equations
Slide 2
When polynomials contain four terms, it is sometimes easier to group like terms in order to factor.
Your goal is to create a common factor.
You can also move terms around in the polynomial to create a common factor.
Practice makes you better in recognizing common factors.
Slide 3
Factoring Four Term Polynomials
Slide 4
Factor by Grouping Example 1:
FACTOR: 3xy - 21y + 5x 35
Factor the first two terms:
3xy - 21y = 3y (x 7)
Factor the last two terms:
+ 5x - 35 = 5 (x 7)
The green parentheses are the same so its the common factor
Now you have a common factor
(x - 7) (3y + 5)
Slide 5
Factor by Grouping Example 2:
FACTOR: 6mx 4m + 3rx 2r
Factor the first two terms:
6mx 4m = 2m (3x - 2)
Factor the last two terms:
+ 3rx 2r = r (3x - 2)
The green parentheses are the same so its the common factor
Now you have a common factor
(3x - 2) (2m + r)
Slide 6
Factor by Grouping Example 3:
FACTOR: 15x 3xy + 4y 20
Factor the first two terms:
15x 3xy = 3x (5 y)
Factor the last two terms:
+ 4y 20 = 4 (y 5)
The green parentheses are opposites so change the sign on the 4
- 4 (-y + 5) or 4 (5 - y)
Now you have a common factor
(5 y) (3x 4)
Slide 7
Slide 8
Factoring Trinominals
When trinomials have a degree of 2, they are known as quadratics.
We learned earlier to use the diamond to factor trinomials that had a 1 in front of the squared term.
x2 + 12x + 35
(x + 7)(x + 5)
Slide 9
More Factoring Trinomials
When there is a coefficient larger than 1 in front of the squared term, we can use a modified diamond or square to find the factors.
Always remember to look for a GCF before you do ANY other factoring.
Slide 10
More Factoring Trinomials
Lets try this example
3x2 + 13x + 4