6.6 1

Section 6.6 Dividing Polynomials

Dividing a Monomial by a Monomial Dividing a Polynomial by a Monomial Dividing a Polynomial by a Polynomial

Long Division Technique Handling Missing Terms

6.6 2

Negative Exponent Rule Quotient Rule for Exponents

261328

2

38

yxyxyx

yx

2

24242271153

75

2113

a

cbcbacba

ba

cba

6.6 3

Dividing a Monomial by a Monomial Remove matching integer factors in the coefficients

2

525

3

6

3

6

5

3

5

3

)7)(5)(2(

)7)(3)(2(

70

42

y

xyx

xy

yx

xy

yx

6.6 4

Dividing a Polynomial by a Monomial

Recall the rule for Using it in reverse, allows adding fractions: a division to be split up:

d

ba

d

b

d

a

d

b

d

a

d

ba

233

6

3

9

3

69 22

xx

x

x

x

x

xx

4

12

44

4

4

8

4

48 22

22

22

22

24

22

43

22

222443

aabba

ba

ba

ba

ba

ba

ba

bababa

6.6 5

Dividing a Polynomial by a Polynomial

Use the long-division process

139

0

13

13

39

09

927

1002713

2

2

2

23

23

aa

a

a

aa

aa

aa

aaaa

127?)139)(13(: 32 aaaaCheck

6.6 6

Dividing with a Remainder

614

124256

32

2

2

4

2124104

31073

xx

xxxxxxx

107?2)4)(3(: 2 xxxxCheck

6.6 7

Practice – Monomial Division

xx

x

xx

73

4

56

3

211518

6.6 8

Practice – Binomial Division

32

15725 2

x

xxx

6.6 9

Practice – Binomial Division w/ Rem

32

2

2

853

xx

xxx

6.6 10

Practice – Binomial Division w/ Rem

14

232

322

29

591

591

aaa

aaa

aaa

6.6 11

What Next? 6.8 Solving Formulas and Variation