Final Review

Simplify

100

3x^-4

3/x⁴

200

(2x²y³)⁴

16x⁸y¹²

300

(5a³b^-2)(-2a^-2b⁶⁾

-10ab⁴

400

(36x³y^-2z⁵)/(24x⁶yz⁵)

3/(2x³y³)

500

[ (12x^-3y³)/(6x^-5y²) ]²

4x⁴y²

Factor

100

x² - 5x + 6

(x - 3)(x - 2)

200

4x² + 9

prime

300

3x³ - 9x² + 30x

3x(x² - 3x + 10)

400

2x² - 3 = 159

x = +/- 9

500

20g³ - 4g² - 25g + 5

(4g² - 5)(5g - 1)

Solve

100

9x² + 12x + 4 = 0

x = -2/3

200

x³ - 16x = 0

x = 0, 4, -4

300

(1/4) + (1/5) = (1/x)

x = 20/9

400

|3x + 2| - 1 = 10

x = 3, -13/3

500

x² + x < 20

(-5 ,4)

Rational Expressions

100

Simplify: (x + 9)/(x² + 15x = 54)

1/(x+6)

200

Simplify: (5x¹⁵/3x⁹) * (6x/20x⁷)

1/2

300

Simplify: (9y³/15y²) / (6y/10y²)

y²

400

Subtract: (x+2)/6 - (x+4)/6

-1/3

500

Subtract: 3x/(x²+x-12) - x/(x² - 16)

x(2x-9)/(x+4)(x-4)(x-3)

Misc.

100

Write in Scientific notation: 340,500

3.405 * 10⁵

200

What is the degree of: 6x⁸yz² + 7x⁵y - 8z²

11 (8 + 1 + 2)

300

Find the domain of: (x - 6)/(x² - 10x + 21)

(-inf, 3) U (3,7) U (7, inf)

400

y varies inversely as x. If y = 20 when x equals 5, what is x when y is 50?

x = 2

500

Find the minimum value of: y = 2x² + 5x + 4

y = 7/8