Algebra II Review

Factoring

1

Simplify the following expression by factoring:

6x³ + 3x²

3x²(2x + 1)

2

Simplify the following expression by factoring:

x² - 16x + 64

(x - 8)²

3

Simplify the following expression by factoring:

(x² - y²)

(x - y)(x + y)

4

Simplify the following expression by factoring:

x² + 4

Not Factorable

5

Simplify the following expression by factoring:

x³ - 125

(x - 5)(x² + 5x + 25)

Imaginary Numbers

1

Which of the following simplifies to -i?

(a) i¹

(b) i²

(c) i³

(d) i⁴

(c) i³

2

What does i⁸³ simplify to?

i³ = -i

3

Simplify the following expression:

15 - 7i - (9 - 24i)

6 +17i

4

Combine the following complex numbers:

(6 - 5i)(4 + 2i)

34 - 8i

5

Divide the following complex numbers:

2 + 5i / 3 + 7i

41 / 58 + 1 / 58i

Absolute Value Inequalities

1

If an absolute value inequality contains a greater than symbol, you should end up with what type of inequality answer?

(a) Compound Inequality

(b) Two Separate Inequalities

(b) Two Separate Inequalities

2

If an absolute value inequality contains a less than symbol, you should end up with what type of inequality answer?

(a) Compound Inequality

(b) Two Separate Inequalities

(a) Compound Inequality

3

Solve the following inequality for the variable and graph the solution:

|4q - 3| < -1

No Solution

4

Solve the following inequality for the variable and graph the solution:

|x + 1| < 10

Solution: (-11, 9)

Graph: See the Board

5

Solve the following inequality for the variable and graph the solution:

|12n - 5| (Less Than or Equal to) 31

Solution: [-13 / 6, 3]

Graph: See the Board

Multiple Radical Signs & Proportions

1

The process used to solve proportion problems involving one fraction on each side of an equation:

(a) Multiplication by the Reciprocal

(b) Cross-Multiplication

(c) Multiplication by the LCD

(b) Cross-Multiplication

2

In order to solve for multiple radical signs, you must isolate the _________ radical sign on one side of the equation.

(a) Simpler

(b) More Complex

(b) More Complex

3

Solve for the variable in the following proportion:

x - 7 / x + 36 = 2 / 5x

x = -8 / 5, 9

4

Solve for the variable by eliminating both radical signs:

√x + √x - 9 = 3

x = 9

5

Solve for the variable by eliminating both radical signs:

√w - 4 + √w + 12 = 8

w = 13