Download A2 – Factoring Review 2

Factoring Patterns
Difference of Perfect Squares
25 x 2  1
Factor out the GCF if there is one
Step 2: Check whether you have difference of squares
Step 3: Use difference of squares pattern to factor
Step 1:
a 2  b2  (a  b)(a  b)
Practice:
x2  4
x2  9
36 x 2  25
36  x 2
9 x 2  16
2 x 2  72
Sum and Difference of Cubes
Perfect cubes: numbers whose factors can be written as a number times itself times itself like
64 = _______
Sum or Difference of Cubes:
Use for two terms that are perfect cubes with a ________ or
__________ sign between the terms.
Sum of cubes: a3 + b3 =
x3 + 27 =
_________________________
Difference of cubes: a3 – b3 =
_________________________
64a3 – 27=
 Always look for a ______________________________, ______ first!
 Check the ______________________ next to see if you can factor any further.
PRACTICE: Factor the following polynomials.
-54x3 + 150
10x 4 – 80x
2x4 + 3x3 + 2x + 3
Perfect Square Trinomials
Perfect square trinomials have the following pattern:
1x2 + 2x + 1
a2
+ 2ab +
b2
= (a + b)(a + b) = _____________
a2 - 2ab + b2 = (a - b)(a - b) = _____________
4x2 – 12x + 9
You can factor them by grouping, but knowing the pattern makes the factoring easier.
**Remember to take out the _____________________________ first!
a)
x2 - 8x + 16
b)
9y2 + 60y + 100
a)________________________
c) 2y4 + 20y2 + 50
b)_________________________
d) 2x2 - 12xy + 18y2
c)________________________
d)_________________________
Additional Practice: Factor completely
x5- x3 + 8x2- 8