Pattern:
Difference of Perfect Squares
Factor: x2 - 36
(x - 6) (x + 6)
Even
powers are perfect squares.
|
Factor: x4 - 16
Re-write to show the perfect squares.
(x2 )2 - 42
Apply the pattern involved with the difference of perfect squares.
(x2 - 4) (x2 + 4)
Continue factoring:
(x - 2) (x + 2) (x2 + 4)
|
Factor: x8 - 256
Again, perfect squares on both sides.
(x4 )2 - 162
Use the same pattern.
(x4 - 16) (x4 + 16)
(x2 - 4) (x2 + 4) (x4 + 16)
(x - 2)(x + 2)(x2 + 4)(x2 + 16) |
Pattern:
Quadratic Trimonial Factoring
Factor: x2 + 3x - 10
(x - 2) (x + 5) |
Factor: x4 + 3x2 - 10
This is the same "quadratic pattern" we listed, but x2 has replaced x.
(x2 )2 - 3(x2) - 10
So replace x with x2 in the factors.
(x2 - 2) (x2 + 5)
|
Factor: x4 - 12x2 + 27
This is the same "quadratic pattern" as:
x2 -12x + 27, so replace x with
x2 in the factors.
(x2 - 9) (x2 - 3)
Continue factoring:
(x - 3)(x + 3)(x2 - 3)
|
Pattern:
Common Factors
Factor: 3x3 - 2x2 - 2x.
x (3x2 - 2x - 2)
Now, the quadratic pattern
x (3x + 1) (x - 2)
|
Factor: 3x6 - 2x5 - 2x4
Use the same approach,
but factor out a larger power.
x4 (3x2 - 2x - 2)
Now, the quadratic pattern
x4 (3x + 1) (x - 2)
|
Factor: 4x9 - 26x8 + 30x7
Same approach with
larger common factor.
2x7 ( 2x2 - 13x + 15 )
Now, the quadratic pattern
2x7 ( 2x - 3) (x - 5) |
