Algebra I Chapter 9 Review

Terms

1

Which of the following polynomial is in standard form?

(a) x² + 5x = -6

(b) x² - x + -1 = 1

(c) x² + 4 = 0

(d) x² + 15x + 56 = 0

(d) x² + 15x + 56 = 0

2

The form x = -b ± √(b² - 4ac) / 2a is also known as what?

Discriminant

3

Quadratic equations are polynomial equations that have the highest exponent of ____.

(a) 2

(b) 1

(c) 4

(d) 3

(a) 2

4

The easiest way to solve a quadratic equation

quadratic formula or factoring

5

The process of taking a given part of a perfect square and completing it is known as _________ the square.

Completing

Factoring

1

Solve the following quadratic equation by factoring: x² -4x - 12.

x = -2, 6

2

Solve the following quadratic equation by factoring: x² + 8x = -16.

x = -4

3

Solve the following quadratic equation by factoring: 3x² = 9x.

x = 0, 3

4

Solve the following quadratic equation by factoring: 9x² - 45 = 4.

x = ± 7/3

5

Solve the following quadratic equation by factoring: x² - 14x - 72.

x = -4, 18

Extracting the Root

1

Which of the following equations should you use extracting the root to solve for the variable?

(a) x² - 81 = 0

(b) x² + 2x - 8

(c) x² - 7x = 0

(a) x² - 81 = 0

2

Solve the following quadratic equation by extracting the root: x² = 121.

x = ± 11.

3

Solve the following quadratic equation by extracting the root: 3x² = 6.

x = ± √2

4

Solve the following quadratic equation by extracting the root: x² + 18 = 54.

x = ± 6

5

Solve the following quadratic equation by extracting the root: (x + 1)² = 3.

x = -1 ± √3

Completing the Square

1

Which of the following equations should you use completing the square to solve for the variable?

(a) x² - 7x - 30

(b) x² - 16 = 0

(c) x² + 3x = 2

(c) x² + 3x = 2

2

Solve the following quadratic equation by completing the square: x² - 6x + 7= 0.

x = 3 ± √2

3

Solve the following quadratic equation by completing the square: x² + 4x - 9 = 0.

x = -2 ± √13

4

Solve the following quadratic equation by completing the square: x² - 6x - 10 = 0.

x = 3 ± √19

5

Solve the following quadratic equation by completing the square: 9x² - 24x - 8 = 0.

x = 4 ± 2√6 / 3

Word Problems

1

Find two numbers whose sum is 22 and whose product is 105.

7 and 15

3

The area of a rectangle is 75 square centimeters with its length 10 centimeters longer than its width. What is the length of the rectangle (A = lw)?

Length = 15 centimeters

5

The area of a rectangle is 405 square meters with its length 12 meters shorter than its width. What are the dimensions of the rectangle (A = lw)?

Length = 15 Meters

Width = 27 Meters