Unit 4 Test Review

Exponent Properties

100

Simplify completely:

a⁵*a⁸

a¹³

200

Simplify completely:

(4²)⁰

1

300

Simplify completely:

2a³b(a⁵b²c)

2a⁸b³c

400

4x²y⁵

______

2xy

2xy⁴

500

(x²y³)⁵

_______

xy

x⁹y¹⁴

Combining and Naming Polynomials

100

Name the following:

3x⁵-6x²+4

Quintic Trinomial

200

Name the following:

-2x²+12x⁴

Quartic Binomial

300

Simplify the following:

(3x³+4x²-2x+1)+(x³-6x²+5)

4x³-2x²-2x+6

400

Simplify the following:

(3x³+4x²-2x+1)-(x³-6x²+5)

2x³+10x²-2x-4

500

Simplify the following:

(3x³+4x²-1)(6x+5)

18x⁴+39x³+20x²-6x-5

Types of Solutions

100

Using the following equation, state the following:

Hint: Use Desmos!

x⁴+x²-42

# possible solutions =

# real solutions =

# double roots =

# complex solutions =

List the real solutions:

# possible solutions = 4

# real solutions = 2

# double roots = 0

# complex solutions = 2

List the real solutions: x = 2.4 and -2.4

200

Using the following equation, state the following:

Hint: Use Desmos!

3x³+9x²-11x-87

# possible solutions =

# real solutions =

# double roots =

# complex solutions =

List the real solutions:

# possible solutions = 3

# real solutions = 1

# double roots = 0

# complex solutions = 2

List the real solutions: x = 2.62

300

Using the following equation, state the following:

Hint: Use Desmos!

-3x⁴-2x³+4x²

# possible solutions =

# real solutions =

# double roots =

# complex solutions =

List the real solutions:

# possible solutions = 4

# real solutions = 4

# double roots = 1

# complex solutions = 0

List the real solutions: x = -1.5, 0, 0, .9

400

Using the following equation, state the following:

Hint: Use Desmos!

5x³+6x²+2

# possible solutions =

# real solutions =

# double roots =

# complex solutions =

List the real solutions:

# possible solutions = 3 

# real solutions = 1

# double roots = 0

# complex solutions = 2

List the real solutions: -1.4

500

Using the following equation, state the following:

Hint: Use Desmos!

5x⁴+2

# possible solutions =

# real solutions =

# double roots =

# complex solutions =

List the real solutions:

# possible solutions = 4

# real solutions = 0

# double roots = 0

# complex solutions = 4

List the real solutions: NONE

Solving by Factoring

100

Solve the following equation by factoring:

x⁴-3x²-10=0

x = 5

x = -2

200

Solve the following by factoring:

2x³-6x²-56x=0

x = 0

x = 7 

x = -4

300

Solve the following by factoring:

x³-8x²+16x=0

x = 0

x = 4

x = 4

400

Solve the following by factoring

x⁴+14x²+45=0

x = +/- 3i

x = +/- i sqrt 5

500

Solve the following by factoring:

x⁴-x²-56=0

x = +/- sqrt 8

x = +/- i sqrt 7

Solving by Roots

100

-2x⁵= 15552

x = -6

200

Solve the following by using roots:

1/3 (x-4)³=9

x = 7

300

Solve the following by using roots:

3(x-4)²-5=7

x = 6

x= -2

400

Solve the following by using roots:

3-(2x+6)⁵=1027

x = -5

500

Solve the following by using roots:

6(x-4)⁴+8= 24584

x = 12

x = -4