Download Factoring Review Notes

August 23, 2012
18g2 and 27g3
15x3 and 30x2
4x
2 and 5y3
August 23, 2012
3
2
9x - 3x + 6x
1. Find the GCF
2. "UN"distribute
3. Multiply to check
August 23, 2012
A. 10y3 + 20y2 - 5y
B. -12x - 8x2
C. 5x2 + 7
August 23, 2012
Factoring Trinomials
Leading Coefficient of 1
*** When factorable, a trinomial will become 2 _________
(
± )( ± )
As I mentioned yesterday, we should always look for a
GCF in any polynomial.
Today however, there will not be any GCFs. We are
just focusing on the method we will call
"EASY" TRIs
August 23, 2012
Ex.1
x2 + 7x + 12
12
Step 1 : List all pairs of numbers that
multiply to equal the constant, 12.
Step 2 : Choose the pair that adds up to the
middle coefficient, _____.
Step 3 : Fill those numbers into the blanks
in the binomials:
(x
x2 + 7x + 12 = ( x + 3)( x + 4)
)( x
)
August 23, 2012
Ex.2
x2 + 2x - 24
-24
Step 1 : List all pairs of numbers that
multiply to equal the constant, -24. (To get
-24, one number must be positive and one
negative.)
Step 2 : Which pair adds up to 2?
Step 3 : Write the binomial factors.
(x
x2 + 2x - 24 = ( x - 4)( x + 6)
)( x
)
August 23, 2012
Ex.3
x2 - 9x + 18
18
Step 1 : List all pairs of numbers that
multiply to equal the constant, 18. (Since
the middle term is negative, both factors will
be negative.)
Step 2 : Which pair adds up to _______?
Step 3 : Write the binomial factors.
(x
x2 - 9x + 18 = ( x - 3)( x - 6)
)( x
)
August 23, 2012
Now it's your turn!
A.
x2 + 10x + 24
B.
x2 - 8x - 20
August 23, 2012
Factoring Trinomials
Leading Coefficient ≠ 1
*** Again when factorable, a trinomial will become 2
_________, however it will no longer just be
( x ± )( x ± )
Again as I mentioned before, we should always look for
a GCF in any polynomial.
Today however, there will not be any GCFs. We are
just focusing on the method we will call
"TRICKY" TRIs or "Divide and Slide"
August 23, 2012
Ex.1
2x2 + 13x + 15
2 · 15 =
Step 1 : List all pairs of numbers that
multiply to a · c.
Step 2 : Still choose the pair that adds up to
the middle coefficient, _____.
Step 3 : TEMPORARILY Fill those numbers
into the blanks in the binomials:
(x
x2 + 7x + 12 = ( x + 3)( x + 4)
)( x
)
August 23, 2012
Step 4 : The DIVIDE - DIVIDE each factor by
the a value, _______.
Step 5 : The SLIDE - reduce each fraction as
always. SLIDE any remaining
denominator in front of the x.
( x + 3 )( x + 10 )
( x + 3 )( x + 5 )
2
SO . . . .
2x2 + 13x + 15 = (2x + 3)(x + 5)
August 23, 2012
Ex.2
3x2 - 11x - 4
3 · -4 =
Step 1 : List all pairs of numbers that
multiply to a · c.
Step 2 : Still choose the pair that adds up to
the middle coefficient, _____.
Step 3 : TEMPORARILY Fill those numbers
into the blanks in the binomials:
(x
x2 + 7x + 12 = ( x + 3)( x + 4)
)( x
)
August 23, 2012
Step 4 : The DIVIDE - DIVIDE each factor by
the a value, _______.
Step 5 : The SLIDE - reduce each fraction as
always. SLIDE any remaining
denominator in front of the x.
( x + 1 )( x - 12 )
( x + 1 )( x - 4 )
3
SO . . . .
3x2 - 11x - 4 = (3x + 1)(x - 4)
August 23, 2012
Ex.3
6x2 - 13x + 6
6·6=
Step 1 : List all pairs of numbers that
multiply to a · c.
Step 2 : Still choose the pair that adds up to
the middle coefficient, _____.
Step 3 : TEMPORARILY Fill those numbers
into the blanks in the binomials:
(x
x2 + 7x + 12 = ( x + 3)( x + 4)
)( x
)
August 23, 2012
Step 4 : The DIVIDE - DIVIDE each factor by
the a value, _______.
Step 5 : The SLIDE - reduce each fraction as
always. SLIDE any remaining
denominator in front of the x.
( x - 4 )( x - 9 )
( x - 2 )( x - 3 )
3
2
SO . . . .
6x2 - 13x + 6 = (3x - 2)(2x - 3)
August 23, 2012
Now it's your turn!
A.
4x2 + 19x + 12
(4x + 3)(x + 4)
B.
3x2 - x - 10
(3x + 5)(x - 2)
August 23, 2012
Perfect Squares
1 4 9 16 25 36 49 64 81 100 121 144
a2 b2 c2 d4 e6 . . . . . x12 y20
z100
August 23, 2012
2
a -4
x2 - y2
August 23, 2012
4a2 - 25
81a2 - 1
August 23, 2012
3
2
4x + 8x - 3x - 6
August 23, 2012
Factoring Checklist
1. No matter how many terms - Check for GCF
2. 2 Terms?
Is it DOTS? YES
NO
(a + b)(a - b)
Done!
3. 3 Terms?
"Easy" or "Tricky"
( ± )( ± )
4.
Grouping
4 Terms?
August 23, 2012
Homework
p. A30 73-119 odds
SKIP 113
ADD 100