This document provides steps and examples for factoring trinomials of the form ax^2 + bx + c. It begins with reviewing special cases like difference of squares and perfect square trinomials. It then outlines a 6-step process for factoring general trinomials: 1) multiply the leading coefficient and constant, 2) find factors of their product that sum to the middle term, 3) rewrite replacing the middle term, 4) factor by grouping, 5) factor out common binomials, 6) check for complete factorization. Examples are provided applying these steps to fully factor trinomials.

1. 1
Today:
Factoring (ax2
+ bx + c) Trinomials
Review of all other factoring
methods/test review
Class Work

2. 2
Complete Factoring Guide
Available

3. 3
Review: Perfect Square
Trinomial
(x² + 8x + 16)
Remember, a PST factors into either a square of
a sum or a square of a difference.
Use the FOIL method to factor the following:
(x² + 4x + 4x + 16) = (x + 4)²
(x² - 16x + 64) (x² - 8x - 8x + 64) = (x - 8)²
(x² - 15x + 36) (x² - 12x - 3x + 36) = Is not a sp. product.
A trinomial with first & third term squares is only a
PST if... 9y3 + 12x2 +
4x
PST or no PST?

4. Steps in factoring completely:
1. Look for the GCF
2. Look for special cases.
a. difference of two
squares
b. perfect square
trinomial
3. If a trinomial is not a
perfect square, look for
two different binomial
factors.
 8t4 – 32t3 + 40t
= 8t(t3 - 4t + 5)
 4x2 – 9y2 =
(2x)2 – (3y)2
 x2 + 8x + 16 =
x2 + 8x + 42 = (x + 4)2
 x2 + 11x – 10
= (x + 10)(x – 1)

5. An organized approach to factoring
2nd degree trinomials
5
Factoring (ax2
+ bx + c) Trinomials

6. Factoring Trinomials
 Use this algorithm (procedure) to take the
guesswork out of factoring trinomials.
 It would be a good idea to write the steps down
once, as they are easy to forget when away
from class
 You can use these steps for any ax2
+ bx + c
polynomial, and for any polynomial you are
having difficulty factoring.

7. Step 1
7
Multiply the leading coefficient and the constant
term

8. Step 2
8
Find the two factors of 24 that add to
the coefficient of the middle term.
Notice the 'plus, plus' signs in the
original trinomial.
Factors of 24:
1 24
2 12
3 8
4 6
Our two factors are 4 &
6

9. Step 3
9
Re-write the original trinomial
and replace 10x with 6x + 4x.
3x2
+ 6x + 4x + 8
Step
4 Factor by Grouping

10. Step
5
10
Factor out the GCF of each pair of
terms
After doing so, you will have...
Step 6 Factor out the common binomial,
check that no further factoring is
possible, and the complete
factorization is..

11. 11
Practice(2)
Factor: 6x3 + 14x2 +
8x
Factor: 4x2 – 20x +
25

14. 9y3 + 12x2 +
4x
Factor 3x5 – 243xFactor 2m2 – 20mn +
50n2
Factor 5x4y – 80x2y3
Factor 5x – 5y + ax - ay