1. Lesson #7
Trinomial Factoring

2. Recall that we have learnt how to factor a polynomial
3 ways so far.
2x3y2 + 4x2y5 – 16x4y3
Common Factoring
=2x2y2
(x + 2y3 – 8x2y)
6ab + 3b – 4a - 2
Group Factoring
=3b
(2a + 1)
- 2
(2a + 1)
=(a + 1)
(3b - 2)
(25x2 – 16y2)
Difference of Squares
Factoring
= (5x – 4y)
(5x + 4y)

3. x2 +bx + c There is another way. If it is a trinomial of the form
where b and c are integers, we use what we call
Munchkin Numbers.
Expand using FOIL
(x + n)(x + m)
=x2
+mx
+nx
+ mn
=x2
+(m+n)x
+ mn
b equals the sum of 2 numbers:
b = m+n
c equals the product of 2 numbers
c = mn

4. eg. 1
Factor these trinomials
1. x2 + 6x + 8
2. x2 + 7x + 12
=(x + )(x + ) 4 2
=(x + )(x + ) 4 3
3. x2 -2x - 15
4. x2 + 7x - 30
=(x - )(x + ) 5 3
=(x - )(x + ) 3 10
5. x2 - 13x + 42
6. a2 -5 ab + 4b2
=(x - )(x ) 7 6
=(a )(a - ) 4b b

5. ax2 +bx + c There is another case for trinomials of the form
Again, a, b and c are integers.
For these problems, use group factoring.
ax2 + bx + c
=ax2
+mx
+nx
+ c
eg. 2
2x2 + 8x + 6
=2x2 + 6x +2x + 6
=2x(x + 3) +2(x + 3)
=(x + 3)(2x+2)

6. eg. 3
Or use a try and error method
1. 2x2 - 5x + 2
2. 3x2 - 5x - 12
=(2x + )(x + ) 1 4
=(3x + )(x - ) 4 3
3. 6x2 -11x + 4
4. 6x2 -29x - 5
=(3x - )(2x - ) 4 1
=(6x + )(x - ) 1 5

7. Homework
All Handout