Factoring
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Transcript of Factoring
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FactoringSession 6:Factoring Special Forms-Perfect Square Trinomial (PST)- -Difference of Two Squares (DoTS)
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Practice Test 2 –NOV. 18
UNIT QUIZ 1 – Nov. 22 GCF, Grouping, DoTS, PST
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OBJECTIVE:
Factorize algebraic expression using DoTS.
Factorize algebraic expression using SoB.
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Factoring Special Forms
Perfect Square Trinomials
222 2 )1 BABABA
222 2 )2 BABABA
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A2 + 2AB + B2 = (A + B)2
A2 - 2AB + B2 = (A - B)2
Perfect Square Trinomials
1st and last terms are perfect squaresmiddle term is 2x the product of the square roots of 1st & last terms
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Factor x2 + 10x + 25
x2 + 10x + 25 = (x)2 + 2(5x) + (5)2 = (x + 5)2
Factor x2 - 12x + 36
x2 - 12x + 36 = (x)2 – 2(6x) + (6)2 = (x - 6)2
A2 +2AB + B2 (A+B)2
Perfect Square Trinomials
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Factor the following:1) 16x2 – 40xy + 25y2
2) 100x2 + 180x + 81
3) 3+6b+3b2
4) 10n2 +100n+250
5) 49n2 −56n+16
6) 200m4 + 80m3 + 8m2
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The Difference of Two Squares
The Difference of Two Squares
The difference of the squares of two terms, factors as the product of a sum and a difference of those terms.
. 22 BABABA
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Factor x2 - 25
x2 - 25 = x2 – 52 = (x + 5) (x – 5)
Factor 9x2 - 4y2
9x2 - 4y2 = (3x)2 – (2y)2 = (3x + 2y) (3x - 2y)
The Difference of Perfect Squares
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Factorize the following:
k2 – 81 = k2 – 92
(k – 9)(k + 9)
Sum and Difference of Two Squares (DoTS)
(x – y)(x + y) = x2 – y2
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Factorize the following:
9a2 – 4
Sum and Difference of Two Squares (DoTS)
(x – y)(x + y) = x2 – y2
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Factorize the following:
25a2 – 64
Sum and Difference of Two Squares (DoTS)
(x – y)(x + y) = x2 – y2
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Factorize the following:
x2 – 16
Sum and Difference of Two Squares (DoTS)
(x – y)(x + y) = x2 – y2
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Factor the following completely
1)4m2 −25
2)9x2 − 1
3)98n2 −200
4)400 − 36v2
5)6x2 – 6y2
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Seatwork: (Notebook)
NSM Book 2: page 91, Exercise 3e:
☞ no. 3, letters f – j ☞ no. 4, letter g – i
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Seatwork: no. 3 (f – j)
f) 81 – 16x2
g) 64 – 9a2
h) –4h2 + 81
i) 2x2 – 18
j) 3x2 – 147
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Seatwork: no. 4 (g – i)
e) 3x2 – 27y2
f) 64a2 – 4b2
g) k2 – ¼ h2
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SEATWORK (Notebook)
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Warm-up: (Notebook)
NSM Book 2: page 92, Exercise 3e:
☞ no. 7, letters a – j
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Factor the following completely1)
2) 8r3 −64r2 +r −8
3) 63n3 +54n2 −105n−90
4) 42mc + 36md − 7n2c − 6n2d
.xxx 2793 23
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PRACTICE TEST25 MINS
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Evaluate the following by factorization:
79 83 – 69 83
= 83 (79 – 69)
= 83 (10)
= 830
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Evaluate the following by factorization:
1032 – 9= (103 + 3)(103 – 3)
= (106)(100)
= 10,600
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Evaluate the following by factorization:
592 – 412
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Evaluate the following by factorization:
682 – 322
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Evaluate the following by factorization:
7.72 – 2.32
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Evaluate the following by factorization:
26.72 – 23.32
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Seatwork: (Notebook)
NSM Book 2: page 92, Exercise 3e:
☞ no. 5, letters f – j☞ no. 6, letters b, d and f
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Seatwork: no. 5 (f – j)
f) 2562 – 1562
g) 8922 – 82
h) 9032 – 972
i) 7632 – 2372
j) 6592 – 3412
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Seatwork: no. 6
b) 5.16 5.6 + 5.16 4.4
c) 587 23 – 23 487
d) 842 – 84 74
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HOMEWORKReview Questions 3 page 108 # 2. a – j # 3. a – j1 whole pad paperSTUDY FOR A UNIT TEST ON TUESDAY