Chapter 5 Review

Polynomials

100

3m^-4n⁴ x 3n

9n⁵/m⁴

200

x^-2y²/xy^-2

y⁴/x³

300

(2x⁴)⁰ / x⁴ * 2x³y^-2

y²/2x⁷

400

2b^-2 / (ba^-4 * 2b^-2)⁴

a¹⁶b² / 8

500

(x^-2y⁴)^-3 / (2x^-4y² * y²)

x¹⁰ / 2y¹⁶

Long/Synthetic Division

100

(n³ - 6n² - 2) / (n-6)

n² - 2/n-6

200

(10x³ + 41x² - 52x - 29) / (x+5)

10x² - 9x - 7 + 6/x+5

300

(90r³ - 66r² -60r + 21) / 9r-3

10r² - 4r - 8 - 1/3r-1

400

(8x³ + 24x² - 32x - 40) / 8x+8

x² + 2x - 6 + 1/x+1

500

(20x⁴ + 50x³ + 8x² + 6x - 35) / (2x+5)

10x³ + 4x - 7

Evaluate Functions

100

k(x) = x² - 4; find k(-5)

21

200

h(x) = x² - 3; find h(6)

33

300

p(a) = a² - a; find p(n²)

n⁴ - n²

400

k(x) = 2x² - 4x; find k(-2x)

8x² + 8x

500

f(x) = 3x³ + 4x² - 3x + 8; find f(-4)

-108

End Behaviors

100

Graph and find end behaviors:

f(x) = -x⁵ + 2x³ - x - 3

f(x)---> +oo as x ---> -oo

f(x) --->-oo as x--->+oo

200

Graph and find end behaviors:

f(x) = x³ - 3x² + 6

f(x)--->-oo as x--->-oo

f(x)--->+oo as x--->+oo

300

Graph and find end behaviors:

f(x) = x² + 8x + 15

f(x)--->+oo as x--->-oo

f(x)--->+oo as x--->+oo

400

Graph and find end behaviors:

f(x) = -x⁴ + 4x² + 3x - 1

f(x)---> -oo as s---> -oo

f(x)---> -oo as x---> +oo

500

Graph and find end behaviors:

f(x) = -4x⁷ - 5x⁴ + 2x² - 6x + 7

f(x)---> +oo as x---> -oo

f(x)---> -oo as x---> +oo

Factoring

100

48x³ - 3

3(4x + 1)(4x - 1)

200

18x² - 50

2(3n + 5)(3n - 5)

300

10k³ + 16k² + 15k + 24

(2k² + 3)( 5k + 8)

400

x³ + 125

(x + 5)(x² - 5x + 25)

500

5x⁴ + 70x² + 240 = 0

2i root 2

-2i root 2

i root 6

-i root 6