GCF
2x2 + 14x
2x(x + 7)
What is the first step when factoring?
Look for a GCF
3x2 - 19x - 14
(3x + 2)(x - 7)
This is the first step of factoring ALWAYS
Look for a GCF
When do you use "factor by grouping"?
when the expression has x3 with 4 terms
What is the template for factoring trinomials?
Two sets of empty parentheses
( )( )
8a - 16
8(a - 2)
-x2 - 4x + 12
-(x - 2)(x + 6)
If a problem doesn't have a GCF, but it does have a number in front of the x2, what do you do?
Magic X (X Method)
x2 - 25
(x - 5)(x + 5)
x3 + x2 - 4x - 4
(x - 2)(x + 2)(x + 1)
What is the template for factoring a difference of two squares?
( + )( - )
Where is the leading coefficient found?
The number in front of the x2 term
4x2 + 24x + 32
4(x + 2)(x + 4)
3x2 - 10x + 8
(3x - 4)(x - 2)
2x2 - 200
2(x - 10)(x + 10)
8x3 - 2x2 + 4x - 1
(2x2 + 1)(4x - 1)
What is the template for factoring a perfect square trinomial?
( )2
6x2 - 30x + 36
6(x - 2)(x - 3)
-3x2 + 30x + 72
-3(x - 12)(x + 2)
-8x2 - 18x - 9
-(4x + 3)(2x + 3)
81x2 - 126x + 49
(9x - 7)2
27x3 - 18x2 - 12x + 8
(3x +2)(3x-2)2
How do you make a Magic X
Multiply first and last, goes on top
Middle coefficient goes on bottom
Leading coefficient is the denominator and goes left and right
-15x2 + 5x
-5x(3x - 1)
4x2 - 16x +15
(2x - 5)(2x - 3)
4x2 - 4x + 15
prime
Define "difference of two squares". How is it factored?
binomial with two perfect squares subtracted
( + )( - )
9x3 - 63x2 + 49x - 343
(x - 7)(9x2 + 49)
What's the most important (and last) step with the Magic X
REDUCE REDUCE REDUCE
bottom goes first, top goes second
If no bottom, then no number in front of x