1. Unit 5 Section 2.6 and 2.9 Factoring Trinomials x2 + bx + c MM1A2.f.
Factor expressions by greatest common factor, grouping, trial and error, and special products limited to the formulas below.
MM1A3.a.
Solve quadratic equations in the form , where a = 1, by using factorization and finding square roots where applicable.

2. Steps Make an X, a really big one!
The top of the x will be the third term of trinomial, sign included.
The bottom of the x will be the coefficient of the second term of the trinomial, sign included.
Ex. x2 + 10x
+10

3. Steps cont’ … x2 + 10x + 24 The +24 represents the product.
The +10 represents the sum.
We need to find two numbers that will multiply to +24 and add to +10.
Factors of 24:
, =25
2, =14
, =11
4, =10

4. Your turn….
x2 + 9x + 14
x2 + 14x + 33
x2 + 16x + 48

5. Rules for factoring trinomials
Set up parenthesis for binomials: ( ) ( )
Make the X to find solutions: X
Rules for signs:
If 3rd term is POSITIVE then the signs in the parentheses are the SAME
(__ + __) (__ + __) or (__ - __) (__ - __)
If 3rd term is NEGATIVE then the signs in the parentheses are the DIFFERENT
(__ + __) (__ - __)
Remember factoring trinomials is FOIL Backwards…

6. Examples: 1. x2 + 18x + 45 = (__ __) (__ __)

7. Factoring 4 terms… Factoring by Grouping
When a Polynomial has 4 terms we try to factor by GROUPING!!
This means that we group the first two terms together and then the second two terms together.
Ex. a2 + a + 2a + 2
Group first two and second two:
(a2 + a) + (2a + 2)

8. Grouping cont…
Once we have grouped our terms, we are going to factor each group separately…
Step (a2 + a) + (2a + 2)
Step 2 a(a + 1) + 2(a + 1)
Step 3 Put the two together
Answer: (a + 2) (a + 1)

9. Examples: 1. m2 – 6m + 2m - 12 2. x2 + x + 5x + 5
3. y3 – 14y2 + y - 14

10. Ticket out the Door Factor the following polynomials: 1. a2 – 2a – 15
2. b2 – 14b + 48
y2 + 11y + 28
x3 + 9x2 + 4x + 36