Lesson 6: Exponents and Polynomials Quiz Solutions

Algebra 1

© 2009 Duke University Talent Identification Program

Page 1 of 3

Show all of your work in order to receive full credit.

1. Simplify.

a) ( ) ( )2 25 9k x kx− −

( ) ( )2 2 3 35 9 45k x kx k x− − =

b) ( ) ( )23 5 46 4x y xy

( ) ( )23 5 4 6 10 4

7 14

6 4 36 4

144

x y xy x y xy

x y

= ⋅

=

c) ( )02x

( )02 1x =

d)

2

2

8

5

w

p

2 2

2 4

8 64

5 25

w w

p p

=

e) 4 7

2 9

12

2

x y

x y−

4 7 2

2 9 2

12 6

2

x y x

x y y

−=

−

f) 0 03 7x x+

0 03 7 3 1 7 1

3 7

10

x x+ = ⋅ + ⋅

= +

=

Lesson 6: Exponents and Polynomials Quiz Solutions

Algebra 1

© 2009 Duke University Talent Identification Program

Page 2 of 3

2. Evaluate.

a) 24

24 16=

b) 24−

24 16− = −

c) ( )24−

( )24 16− =

3. Complete the indicated operations. Simplify answers as much as possible.

a) ( ) ( )3 2 35 2 3 4 6 4 1x x x x x+ − + − − +

( ) ( )3 2 3 3 2 3

3 2

5 2 3 4 6 4 1 5 2 3 4 6 4 1

2 3

x x x x x x x x x x

x x x

+ − + − − + = + − + − + −

= − + + +

b) ( )4 2 3k k +

( ) 24 2 3 8 12k k k k+ = +

c) ( ) ( )2 3 3 4x x+ −

( ) ( ) 2

2

2 3 3 4 6 8 9 12

6 12

x x x x x

x x

+ − = − + −

= + −

Lesson 6: Exponents and Polynomials Quiz Solutions

Algebra 1

© 2009 Duke University Talent Identification Program

Page 3 of 3

4. Complete the indicated operations. Simplify answers as much as possible.

a) ( )25 3m +

( )2 25 3 25 30 9m m m+ = + +

b) ( ) ( )4 5 4 5m m− +

( ) ( ) 24 5 4 5 16 25m m m− + = −

c) ( ) ( )25 3 2c c c− + −

( ) ( )2 3 2 2

3 2

5 3 2 3 2 5 15 10

2 17 10

c c c c c c c c

c c c

− + − = + − − − +

= − − +

d) ( ) ( )4 210 3 12 3r r r r− + + ÷ +

4 3 2

4 3

2 2

+ 2 2

2

+ 2

-

3 0 10 3 12

3

3 10

3 9

3

3

6 12

6 18

r r r r r

r r

r r

r r

r r

r r

r

r

− −

+

+

−

+ + − + +

+

− −

− −

− +

− −

+

+

3 23 6

6

r r r− − +

−

Answer: 3 2 63 6

3r r r

r− − + −

+