Download Factoring-Special Cases

February 15th, 2012
Factor the following. Determine whether to factor by GCF, Easy Trinomial (ET),
Hard Trinomial (HT), Factoring By Grouping (FBG)—or a combination! Write to
the side the methods you used! First example is done…
1) 20x2 - 115x - 30
__GCF
__HT_
2)
x2 + 4x – 96
______ ______
3) 14a2 b - 63a5 b6
______ ______
4)12x3 +3x2 +20x +5
______ ______
• Multiply (x – 2) (x + 2)….
• This product is a little different than the rest.
What is it missing?
• A middle term!
• If given x2 – 4, and asked to factor, how
could you set this up using what you know
already?
• What is the middle coefficient, b ?
• What is the last number, c ?
• Can you find two numbers that add to be zero
and multiply to be – 4 ?
-4
0
2
a -
2
b
= (a - b) (a + b)
2
2
x - 2 = (x - 2) (x + 2)
2
x – 4 = (x - 2) (x + 2)
This only works for
the DIFFERENCE,
not sum/addition!
Factor x2 - 9 = (a - b) (a + b)
What number squared is 9?
So… (x - 3) (x + 3)
Check your answer by FOIL or box!
• What if there is a coefficient in the front?
4x2 – 25
It works the same way!
What number squared is 4? 25?
(2x - 5) (2x + 5)
1) x2 – 144
2) w2 – 64
3) 16m2 – 49
4) 9k2 – 400
• Multiply (x + 6) (x + 6)….
• What do you notice about the product?
Can you find a pattern?
a2 + 2ab + b2 = (a + b) (a + b)
x2 + 8x + 16 = (x + 4) (x + 4)
x2 +2(1)(4) + 42 = (x + 4) (x + 4)
If you are having trouble
recognizing the pattern, practice
factoring like we did earlier.
1) x2 + 6x + 9
2) x2 + 10x + 25
2
a -
2ab +
2
b
= (a - b) (a - b)
x2 - 14x + 49= (x - 7) (x - 7)
x2 – 2(1)(7) + 72 = (x - 7) (x - 7)
Why do we ADD b2?
1) x2 - 10x + 25
2) x2 - 20x + 100
• What if there is a coefficient in the front?
4x2 – 12x + 9
What number squared is 4? 9?
(2x - 3) (2x - 3)
Why is there a 12x in the middle?
Check your answer!
1) 4x2 + 36x + 81
2) 25z2 + 40z + 16
1) 9n2 – 42n + 49
2) 36d2 – 60d + 25
• Is 24g2 -6 a difference of two squares?
• What should I do first?
• GCF =
• So….
24g2 – 6 = 6 (4g2 – 1)
= 6 (2g - 1) (2g + 1)
Now factor using
difference of squares!
1) 27x2 + 90x + 75
2) 8z2 - 64z + 128
• Find the side length of the square!
Area = 25r2 - 30r + 9
Factor: c10 – 30c5d2 + 225d
If 49x2 – kx + 36 is a perfect square trinomial,
what is the value of k?
• Workbook pg. 247 Factoring Special Cases
• COMPLETE ALL ODDS!
• Workbook pg. 248
• Choose any 5 questions between #26-43