Polynomial Functions

Add., Subt., Mult., Div.

100

(8x³-6x⁴+3) - (3x³-3+8x⁴)

-14x⁴+5x³+6

200

-3x(5x+1)(8-2x)

30x³-114x²-24x

300

(1-2n)²-7n(n²-2)

-7n³+4n²+10n+1

400

(-42x¹⁰y⁵ + 12x⁸y³ - 6x²y) / (6x²y)

-7x⁸y⁴+2x⁶y²-1

500

(16a⁴ - 40a² + 24a) / (12a³)

(4a/3) - (10/3a) +(2/a²)

Graphing Polynomials/Zeros and Multiplicity

100

What is the relative maximum of the equation 

f(x) = - x³ + 3x²

(2, 4)

200

What is the relative minimum of the equation 

f(x) = - x⁴ + 4x² - 3x - 2

(0.41, -2.59)

300

What is the range of the equation 

f(x) = - x⁴ + 4x² - 3x - 2

y | y</= 6.5   or   (- infinity, 6.5)

400

What is the decreasing interval of the equation 

f(x) = 2x³ - 4x² - x

(- 0.12, 1.45)

500

What are the zeros AND their multiplicities AND the effect it has on the graph of the polynomial

f(x) = 3x³ - 21x² - 54x

0, mult. 1, intersects

9, mult. 1, intersects

-2, mult. 1, intersects

Factoring Polynomials

100

k³ - 27

(k - 3)(k² + 3k + 9)

200

3m⁴ - 48n²

3(m² + 4n)(m² - 4n)

300

m⁶ - 7m⁴ - 18m²

m²(m +3)(m - 3)(m² +2)

400

9y⁶ + 6y⁴ +y²

y²(3y² + 1)²

500

3p³ + 5p² - 12p - 20

(p+2)(p-2)(3p+5)

Solving Polynomials

100

9x⁴ - 16 = 0

x = +- 2sqrt(3) / 3

x = +- 2isqrt(3) / 3

200

x3 + 512 = 0

x = -8

x = 4 +- 4isqrt(3)

300

2x³ - 16x² - 40x = 0

x = -2

x = 0

x = 10

400

x³ + 3x² = 24x + 72

x = -3

x = +- 2sqrt(6)

500

4x⁴ + 35x² - 9 = 0

x = +- 1/2

x = +-3i

Dividing Polynomials

100

(3k² - k - 20) / (k + 2)

3k - 7 - (6/(k+2))

200

(x³ + 2x² - 22x - 45) / (x+5)

x² - 3x - 7 - (10/(x+5))

300

(2c³ + 13c² + 24c + 8) / (c+3)

2c² + 7c + 3 - (1/(c+3))

400

(2x³ - 14x + 10) / (x + 3)

2x² - 6x + 4 - (2/(x+3))

500

(p⁴ - 7p² - 32p - 15) / (p - 4)

p³ + 4p² + 9p + 4 + (1/(p-4))