Math class 3/28

Factoring

100

What is this mathematical phenomenon called?

a² - b² = (a + b)(a - b)

Difference of squares

200

What is this phenomenon called?

a³ - b³ = (a - b)(a² + ab + b²)

Difference of cubes

300

Factor:

x² - 2x + 8

(x - 4)(x + 2)

400

Solve:

3x² + 9x + 6

x = {-3, -6}

500

EXTENDED TIME

Solve:

2x⁴ - 18x³ + x² - 9x

x = {0, 9}

Multiplying/ Dividing Rationals

100

Find the product:

3x/2 X 2x/3

6x

200

Find the product:

4x/x² X x²/2x

4x²

300

Find the quotient:

[(x² + 4x)/(4x - x²)] / [(x² - x) / (x² - 2x)]

(-x + 2) / -x

400

Find the quotient:

[(3x³ − 6x² + 9x)/(2x² - 4x)] / [(4x² - 8x)/(6x3−12x2+18x)]

(3x³ − 6x² + 9x)/[4(x−2)²]

500

EXTENDED TIME + DOUBLE JEOPARDY

Find the quotient:

[(4x³ - 8x² + 12x)/ (2x² - 4x + 6)] / [(6x⁴ - 12x³ + 18x²)/(3x³ - 6x² + 9x)

1

Simplifying Rationals

100

Simplify: 

18a/4a²

9/2a

200

Simplify:

2x³/4x²

x/2

300

Simplify:

(6x² - 12x)/3x

2(x - 2)

400

Simplify:

(5x² + 10x)/(x² + 2x)

5

500

EXTENDED TIME

Simplify:

(8x⁷ - 16x⁶ + 24x⁵)/(4x⁶ - 8x⁵ + 12x⁴)

2x

Subtracting/Adding Rationals

100

Find the sum:

1x²/x + 2/x

x +2

200

Find the sum:

2x³/x + x²/x

3x²

300

DOUBLE JEOPARDY

Find the sum:

(x + 3)/(x + 2) + 2x/(x+2)

(3x + 3)/(x + 2)

400

Find the difference:

(x + 3)/(2x - 5) - (x + 3)/3x

(x² + 8x + 15)/[(2x−5)(3x)]

500

EXTENDED TIME

Find the sum:

3/(x² + 2x) + 5/(x² - 4)

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

Logs

100

Solve:

log₂(x) = 4

x =16

200

Solve:

log₃(x)=log₃(27)

x = 27

300

Expand the expression:

log₂(x²y³)

2 X log₂(x)+3 X log₂(y)

400

Solve:

log₂(x²+5x) − log₂(x+3)= 3

x = 8

500

EXTENDED TIME

Solve:

2 X log₃(x) + log₃(x−4) = 4

x = {0, 1, 3}