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College Algebra K/DCFriday, 26 September 2014
• OBJECTIVE TSW factor using (1) the pattern of difference of two squares, and (2) the pattern of the sum and difference of two cubes.
• ASSIGNMENTS DUE TODAY– Sec. R.4: pp. 40-41 (1-16 all, 18-23 all) wire basket
– Sec. R.4: p. 41 (51-60 all + my problems) black tray (will be done in class today)
• ASSIGNMENT DUE MONDAY– Sec. R.4: p. 41 (25-45 odd)
• QUIZ ON MONDAY– Factoring polynomials by GCF, Grouping, and Trinomials
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R-2
Factoring PolynomialsR.4Factoring Binomials – Differences of Squares
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Factoring Differences of Squares
REMEMBER:
When factoring, ALWAYS look for a GCF 1st.
Then, look for a pattern:
1. Are there four terms?
If it factors, you’ll probably use grouping.
2. Are there three terms?
If it factors, you’ll probably factor using guess and check or the box method. R-3
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Factoring Differences of Squares
3. Are there two terms?
If there are, is the problem a difference (subtraction)?
a. Are the two terms perfect squares?
If they are, then use the pattern of differences of squares.
R-4
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Factoring Differences of Squares
If there is a GCF, factor it out first:
Be careful:
R-5
2 2 a b a ba b
2 2 2 2ca cb c a b
2 2 does not factor!!!a b
c a b a b
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R-6
Example Factoring Differences of Squares
Factor each binomial:
(a)
(b)
(c)
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R-7
Example Factoring Differences of Squares
Sometimes, you may have to factor more than once.
4 4256 625k m
2 216 25 4 5 4 5k m k m k m
2 2 2 216 25 16 25k m k m
Always factor completely (factor until you can’t factor anymore)!
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College Algebra K/DCTuesday, 29 September 2015
• OBJECTIVE TSW factor using the pattern of the sum and difference of two cubes.
• ASSIGNMENT DUE– Sec. R.4: pp. 38-39 (25-45 odd, 51-60 all) wire basket
• ASSIGNMENT DUE TOMORROW/THURSDAY– Sec. R.4: pp. 39-40 (61-70 all, 93, 95) today’s assignment
• ASSESSMENT TOMORROW/THURSDAY– Polynomials
• Partners (I choose)
– Thursday: 6th Period Only – ‘C’ Lunch!!!
• TEST ON TUESDAY, 10/07/2015– Factoring
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Factoring PolynomialsR.4Factoring Sums and Differences of Cubes
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Sums or Differences of Cubes
The key is to recognize that the two terms are perfect cubes and then determine their cube roots.
Perfect Cube Cube Root
8 2327a 3a
6 121000g k 2 410g k
3 9343x y 37xy
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Sums or Differences of Cubes
Recall the pattern for factoring a difference of squares:
The pattern for factoring a difference (subtraction) of cubes is similar:
If the expression is a sum (addition):
2 2a b a b a b
3 3 2 2a b a b a ab b
3 3 2 2a b a b a ab b
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Sums or Differences of Cubes
To remember the signs, just use SOAP:• Same Opposite Always Positive
3 3 2 2a b a b a ab b
3 3 2 2a b a b a ab b
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Example Factoring Sums or Differences of Cubes
Factor each polynomial:
(a)
(b)
222 2 2s s sr r r
2 22 2 4r s r rs s
210 10 100t t t
2 210 10 10t t t 3 310t
33 2sr
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Example Factoring Sums or Differences of Cubes
Factor each polynomial:
(c)
3 4 6 3 4 85 6 25 30 36u v u u v v
3 3435 6u v
3 3 32 24 4 46 6 65 5 5v v vu u u
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Example Factoring Sums or Differences of Cubes
Factor each polynomial:
(d)
prime
3 227 8k p
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R-16
Assignment: Sec. R.4: pp. 39-40 (61-70 all, 93, 95)Write the problem and factor each polynomial.
3 6 ) 81 a 3 26 72) r 3 126 ) 5 23 7x
3 3 8 764) 2m n 9 6 27 565) 12y z 9 12 276 ) 646 z y
3 276 ) 29 m n 3 ) 276 38 b 3 6 2167) 6r
3 12570) 4a b 3 3 1000 3 393) 4x y 6 1259 ) 15 2 6m