RULES FOR FACTORING
REVIEW OF CMF
6x2 – 12 = 6
3x2 – 6x + 18 = 3
10x3 + 15x2 – 5x = 5x
(x2 – 2)
(x2 – 2x + 6)
(2x2 + 3x – 1)
D.O.T.S.Difference Of Two Squares
Perfect Squares
x2
y2
a2
b6
9
16
49
100
9x2
25y2
81x2y2
4x4y6
Differencemeans subtract
So, examplesof DOTS:
x2 – 16or
4a2 – 25b2
D.O.T.S.Difference Of Two Squares
DOTS always factors the same way.
(Square root of the first + square root of the last) times(Square root of the first – square root of the last)
x2 – 16 =
Example:
(x + 4) (x – 4)
D.O.T.S.Difference Of Two Squares
4a2 – 25b2 = (2a + 5b)
b2 – 49 = (b + 7)
9x2y2 – 64b6 = (3xy + 8b3)
(2a – 5b)
(b – 7)
(3xy – 8b3)
P.S.T.Perfect Square Trinomial
x2 + 6x + 9
How to identify:
☺Square root of the first
x☺Square root of the last
3☺Multiply them3x
☺Double the result
☺Is it the same as the middle term?(disregard sign)
☺1st & last term must be perfect squares
?
YES!
P.S.T.Perfect Square Trinomial
x2 + 6x + 9
How to identify:
☺Square root of the first
x☺Square root of the last
3☺Multiply them3x
☺Double the result
☺Is it the same as the middle term?(disregard sign)
☺1st & last term must be perfect squares
?
THIS
IS A PST
P.S.T.Perfect Square Trinomial
x2 + 6x + 9
How to factor
Square root of the first
(xSquare root of the last
2Sign of the second term 3)
Quantity squared
+
P.S.T.Perfect Square Trinomial
4m2 – 20m + 25
How to factor
Square root of the first
(2mSquare root of the last
2Sign of the second term 5)
Quantity squared
–
FLASH CARDSFactoring Practice
5x2 + 10xyRECALL STEPS!
CMF
BINOMIAL?
TRINOMIAL
GUESS
5x(x + 2y)DOTS
PST
1.
2.
3.
FLASH CARDSFactoring Practice
x2 – 9y2RECALL STEPS!
CMF
BINOMIAL?
TRINOMIAL
GUESS
(x + 3y)(x – 3y)DOTS
PST
1.
2.
3.
FLASH CARDSFactoring Practice
4x2 – 28x + 49RECALL STEPS!
CMF
BINOMIAL?
TRINOMIAL
GUESS
(2x – 7)2DOTS
PST
1.
2.
3.
FLASH CARDSFactoring Practice
a2 – 2a – 15RECALL STEPS!
CMF
BINOMIAL?
TRINOMIAL
GUESS
(a – 5)(a + 3)DOTS
PST
1.
2.
3.