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Transcript
Algebra 2
Unit 9 In Class Factoring Practice WS
Name: __________________________
Period: __________
This packet includes:

factoring notes

sample problems of each type
FACTORING
Two Terms
Three Terms
More than
Three Terms
GCF
GCF
GCF
Difference of
Perfect Squares
Trinomial
LC =1
Difference of
Perfect Cubes
Trinomial
LC not =1
Sum of
Perfect Cubes
Factoring Notes
1)
2)
3)
4)
5)
6)
7)
8)
Take out the greatest common factor (reverse distributive property)
Difference of perfect squares
Sum of perfect cubes
Difference of perfect cubes
Perfect square trinomial
Trinomial with leading coefficient of 1
Trinomial with leading coefficient not equal to 1
Grouping
Grouping
ALWAYS FIRST look for a GCF in all terms. If there is, pull out the GCF in front. In the parenthesis
goes what’s left over.
Ex: 15xy2 – 10 x3y + 25 xy3 = 5xy( 3y – 2x2 + 5y2)
IF THERE ARE 2 TERMS: it could be…..
Difference of perfect squares: Your answer is the product of two binomials. Take the square root of
each term. One binomial is Plus and the other binomial is Subtract.
Ex: 4x2 – 25y4 = (2x + 5y2)(2x – 5y2)
Sum or Difference of a perfect cube: Your answer is a binomial times a trinomial. Binomial part is the
cube root of each original term with the same sign. For the Trinomial part only look at the new binomial (not the
original problem and use SOFAS). Square the first term, Opposite sign, multiply the First term by the second
term, Always positive, Square the second term.
Ex: 8x3 – y3 = (2x – y)(4x2 + 2xy + y2)
IF THERE ARE 3 TERMS: it could be…..
Perfect square trinomial if the first and last terms are perfect squares and the middle term is twice the
product of the square root of the first and last. Find numbers that multiply to = -12 and add to = -4. The numbers
are –6 and + 2.
Ex: x2 + 6x + 9 = (x + 3)2
and
A trinomial with leading coefficient of 1. You must find two numbers that multiply to equal the last term
add to equal the middle term. Your answer is the product of two binomials.
Ex: x2 – 4x – 12 = (x + 2)(x – 6)
A trinomial with leading coefficient not equal to 1. Your answer will be the product of two binomials.
There are a few different methods that teachers often use. “The Magic Box”, “T-chart”, guess and check. I will
do the divide, reduce and swing method here.
Ex: 3x2 + 10x + 8
(x + 6)(x + 4)
* Two numbers that multiply to be 24 and add to be 10 are 6 and 4.
* Use these two numbers with correct sign and write as binomials
6
4
( x  )( x  )
3
3
4
( x  2)( x 
3)
* Divide the plain numbers (6 and 4) by the leading coefficient (3).
(3x + 4)(x + 2)
* Swing the denominator of any unreduced fraction up to the front of that
binomial.
* Reduce the fraction if possible.
IF THERE ARE 4 TERMS:
Grouping. Group two terms together and another two terms together leaving an addition sign in between
the two binomials. Take out a GCF from each binomial. Your goal is that inside the parenthesis are identical. If
this happens then you rewrite your answer as the product of two binomials.
Ex: 12ac + 21ad + 8bc +14bd
Step 1.
(12ac + 21ad) + (8bc + 14bd)
Step 2.
3a(4c + 7d) + 2b(4c + 7d)
Step 3.
(3a + 2b)(4c + 7d)
Use the attached “factoring notes” to brush up on your factoring skills. Factor completely.
EXPRESSION
FACTORED FORM
TYPE
1.
16m2n + 12mn2
GCF
2.
x2 – 2x
GCF
3.
x2 – 25
Diff. of Perfect Sq’s
4.
x4 – 1
Diff. of Perfect Sq’s (twice)
5.
3a2 – 27b2
Combo: GCF & Per. Sq’s
6.
x3 + 125
Sum of Perfect Cubes
7.
a3 – b6
Diff. of Perfect Cubes
8.
x3 + 27
Sum of Perfect Cubes
9.
x2 + 8x + 16
Perfect Square Trinomial
10.
2t3 + 32t2 + 128t
Combo: GCF & Trinomial
11.
a 3b 3  c 6
Diff. of Perfect Cubes
WORK
12.
4w 2  12wr  9r 2
Perfect Sq. Trinomial
13.
8x3  y 3
Sum of Perfect Cubes
14.
20 x 2  60 x  35
Combo: GCF & Trinomial
200  17 r  r 2
15.
Trinomial
DO NOT SWITCH THE ORDER!
16.
17.
18.
6x2 + 10x – 4
Combo: GCF & Trinomial
4 x 2  8 x  4 xy  8 y
Combo: GCF & Grouping
21 – xy – 7y + 3x
Grouping