Algebra 2A Review

Factoring

100

x² - 81

(x + 9)(x - 9)

200

a³ + b³

(a + b)(a² - ab + b²)

300

32x² - 72

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

400

27x³ - 125

(3x - 5)(9x² + 15x + 25)

500

16x² - 24xy + 9y²

(4x - 3y)²

Complex Numbers

100

(16 + 2i) - (-7 + 4i)

23 - 2i

200

(8 - 6i) + 2(-3 + 3i)

2

300

12i(6 - 3i)

36 + 72i

400

(6 + i)(6 - i)

37

500

(5 - 3i)²

16-30i

Quadratics

100

What is the ordered pair of the vertex:

y = -2(x - 3)² - 4

(3, -4)

200

What are the solutions (zeros/x-intercepts):

y = x² + 5x + 6

x = -3

x = -2

300

What is the ordered pair of the vertex:

y = x² + 5x + 6

(-2.5, -.25)

400

What's the difference?

y = 2(x - 3)² + 5

y = 2(x + 3)² + 5

Vertices are different

(3, 5) and (-3, 5)

500

What are the solutions:

y = 6x² - 3x + 4

3+-i (sqrt 87)/12

Simplify Radicals

100

Square Root of 16x⁶

4x³

200

Square Root of 24x³y⁵

4xy²(square root 6xy)

300

Cube Root of 216x⁹

6x³

400

Cube Root of 135x⁷y⁶

3x²y²(cube root 5x)

500

Fourth Root of 256x²y⁶z⁵

4yz(fourth root x²y²z)

Solving and Simplifying Equations

100

(x² + 3)(x + 4)

x³ + 4x² +3x + 12

200

Square root of (x - 3) = 6

x = 39

300

(x + 2)^3/4 = 8

x = 14

400

(3x³ - 4x)(2x² + 2x - 5)

6x⁵ + 6x⁴ - 23x³ - 8x² + 20x

500

-3 + (2x + 5)^3/2 = 122

x = 10