College Algebra K/DCThursday, 24 September 2015

• OBJECTIVE TSW factor polynomial expressions by (1) GCF, (2) grouping, and (3) trinomials.

• The tests are not graded.

• TODAY’S ASSIGNMENT– Sec. R.4: p. 38 (1-16 all, 19-24 all)– Due tomorrow, Friday, 25 September 2015.

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Factoring PolynomialsR.4Factoring Out the Greatest Common Factor ▪ Factoring by Grouping ▪ Factoring Trinomials

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Example Factoring Out the Greatest Common Factor

Factor out the greatest common factor from each polynomial.

(a)

(b)

When factoring variables, factor the smallest exponent.

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Example Factoring Out the Greatest Common Factor

Factor out the greatest common factor from the polynomial.

(c)

22 2 12 2 8 2 3xx x

This now needs to be simplified.

GCF = 2(x – 2)

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Example Factoring By Grouping

Factor by grouping.

24 n m n

Factor each individual parentheses.

Now factor out the parentheses.

First, group the terms into parentheses.

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Example Factoring By Grouping

Factor by grouping.

23 5 3 2y y

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Example Factoring By Grouping

Factor by grouping.

23 5s r

The middle term is negative . . .

. . . causing the next sign to switch.

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Example Factoring (GCF and Grouping)

Factor the expression.

2 2 6 30 8 4a) 0x y x xy x

2 3 15 4 20x xy x y

2 3 15 4 20x xy x y

2 3 5 4 5x x y y

2 5 3 4x y x

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Example Factoring (GCF and Grouping)

Factor the expression (on your own).

2 72 12 54b) 9a ab b b

23 24 4 18 3a ab b b

23 24 4 18 3a ab b b

3 4 6 3 6a b b b

3 6 4 3b a b

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Assignment: Sec. R.4: p. 38 (1-16 all, 19-24 all) Due on Friday, 25 September 2015.

• Use a separate sheet of notebook paper.

• This will be the last assignment for which you get a hard copy.

College Algebra K/DCFriday, 25 September 2015

• OBJECTIVE TSW factor (1) trinomials, and (2) differences of squares.

• ASSIGNMENT DUE (wire basket)– Sec. R.4: p. 38 (1-16 all, 19-24 all)

• TODAY’S ASSIGNMENT (due on Tuesday, 09/29/15)

– Sec. R.4: pp. 38-39 (25-45 odd, 51-60 all)

• QUIZ: Factoring GCF, Grouping, Trinomials on Monday, 09/28/15.

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Factoring PolynomialsR.4Factoring Trinomials ▪ Factoring Binomials – Differences of Squares

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Example Factoring Trinomials (Guess and check Method)

Factor , if possible.

The positive factors of 5 are 5 and 1.

The factors of –12 are –12 and 1, 12 and – 1,

–6 and 2, 6 and –2, –4 and 3, or 4 and –3.

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Example Factoring Trinomials (Guess and check Method)

Try different combinations:

Factor . –12 and 112 and – 1–6 and 26 and –2–4 and 34 and –3

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Example Factoring Trinomials (Box Method)

Factor , if possible.

12t 2

–3

1st: Put the squared term in the upper left, constant term in the lower right.

2nd: Multiply 12 and –3: –36. “Are there 2 factors of –36 that add up to –5?”

3rd: Yes, –9 and 4. Place these in the remaining two boxes (either order).

–9t

4t

Multiply 12 and –3.

“Are there two factors of –36 that add up to –5?”

= –36

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Example Factoring Trinomials (Box Method)

Factor , if possible.

12t2

–3

4th: Factor each row and column.

5th: Write the answer: (3t + 1)(4t – 3)

–9t

4t

3t

1

4t –3

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Example Factoring Trinomials (Box Method)

Factor .

(3)(16) = 48 There are not two factors of 48 that equal –15.

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Example Factoring Trinomials (Box Method)

Factor . HINT: Is there a GCF?

2 224 42 15 3 8 14 5x x x x

8x2

5

10x

4x

2x

1

4x 5

224 42 15 3 2 1 4 5xx x x

(8)(5) = 40

Are there two numbers whose product is 40 and sum is 14?

Don’t forget the 3!!!

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Example Factoring Perfect Square Trinomials

Factor each trinomial:

(a)

(b)

Perfectsquare

Positive perfectsquare

249 7x x 24 2y y

Is the middle term2(7x)(2y)?

YES!

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-21

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)!

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Assignment (09/25/2015)

• Sec. R.4: pp. 38-39 (25-45 odd, 51-60 all)– Write the problem and factor.– Due Tuesday, 29 September 2015.

• QUIZ: Factoring GCF, Grouping, Trinomials on Monday, 09/28/15.