1. Factoring Trinomials Mrs. Unger’s Method…
The Box Method + Part of the Master Product Method

2. Ex1: k2 + 9k + 20 k +4 k k2 4k +5 5k 20 1.) Draw box
2.) Write 1st term in 1st box, and 3rd term in 4th box.
3.) Find Master Product
(1)(20) = 20
1, 20
2, 10
4, 5
4.) List factors of MP to find two whose sum equals “b”.
5.) Put factors in remaining boxes with variable.
6.) Factor out GCF in each row.
7.) Factor out GCF in each column.
8.) Write your answer!
(k + 5)(k +4)

3. Ex2: 2x2 – 11x + 12 x -4 2x 2x2 -8x -3 -3x 12 1.) Draw box
2.) Write 1st term in 1st box, and 3rd term in 4th box.
3.) Find Master Product
(2)(12) = 24
-1, -24
-2, -12
-3, -8
-4, -6
4.) List factors of MP to find two whose sum equals “b”.
5.) Put factors in remaining boxes with variable.
6.) Factor out GCF in each row.
7.) Factor out GCF in each column.
8.) Write your answer!
(2x – 3)(x – 4)

4. Ex3: –10 + 24z – 8z2 –8z2 + 24z – 10 –2(4z2 – 12z + 5) 2z -1 2z 4z2
Before we can do anything, we have to rearrange.
–8z2 + 24z – 10
And then we have to take out the GCF.
GCF = –2
–2(4z2 – 12z + 5)
(4)(5) = 20
-1, -20
-2, -10
-4, -5 2z -1 2z
4z2
-2z –2
(2z – 5)(2z – 1) -5
-10z 5
But don’t forget that -2 we took out earlier!

5. Ex4: 15x2 + 13xy + 2y2 Ok, here we go… 5x +y 3x 15x2 3xy +2y 10xy 2y2
But what happens when we have TWO variables???
It’s no big deal. It’s the same method.
Check for the GCF, first.
GCF = Well that doesn’t help!
Ok, here we go…
(15)(2) = 30
1, 30
2, 15
3, 10
5, 6 5x +y 3x
15x2
3xy
(3x + 2y)(5x + y)
+2y
10xy
2y2

6. Ex5: a2 – 2a – 35 Pretty easy, right??? a +5 a a2 5a -7 -7a -35
Ok, last example.
I wanted to show you one where you have to factor out a negative for your answer.
Check for the GCF, first.
GCF = Well that doesn’t help!
(1)(-35) = -35
1, -35
-1, 35
5, -7
-5, 7 a +5 a a2 5a
(a – 7)(a + 5) -7
-7a
-35
Pretty easy, right???

7. Happy Factoring!!!