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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Factoring PolynomialsR.4Factoring Binomials – Differences of Squares

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

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.

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Factoring Differences of Squares

If there is a GCF, factor it out first:

Be careful:

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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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Example Factoring Differences of Squares

Factor each binomial:

(a)

(b)

(c)

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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)!

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

Factoring PolynomialsR.4Factoring Sums and Differences of Cubes

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

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

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

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

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

Example Factoring Sums or Differences of Cubes

Factor each polynomial:

(d)

prime

3 227 8k p

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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