Exploring Adding and Subtracting Rational Expressions

The video tutorial covers solving quadratic equations using the method of completing the square. It begins with an introduction to perfect square trinomials and demonstrates how they can be factored into binomials squared. The tutorial then explains how to solve these equations using square roots, emphasizing the need to consider both positive and negative roots. The process of completing the square is detailed, with step-by-step instructions and examples, including cases with irrational solutions.

What is the repeated factor of the trinomial x² + 8x + 16?

• x + 16

• x + 4

• x + 8

• x + 2

How can the trinomial x² - 18x + 81 be factored?

• (x - 9)²

• (x - 18)²

• (x + 18)²

• (x + 9)²

What are the solutions for the equation (x + 2)² = 25?

• x = 2 and x = -2

• x = 7 and x = -3

• x = 5 and x = -5

• x = 3 and x = -7

What is the first step in completing the square for the equation x² + 8x - 7 = 0?

• Add 7 to both sides

• Divide both sides by 2

• Subtract 7 from both sides

• Multiply both sides by 2

What value should be added to both sides of the equation x² + 8x = -7 to complete the square?

• 64

• 16

• 8

• 4

What are the solutions for the equation (x - 6)² = 9?

• x = 6 and x = -3

• x = 3 and x = -3

• x = 9 and x = 3

• x = 6 and x = -6

What is the simplified form of the square root of 18?

• 3√2

• 2√3

• √9

• √36

What are the solutions for the equation (x + 8)² = 18?

• x = 8 ± √18

• x = 8 ± 3√2

• x = -8 ± √18

• x = -8 ± 3√2

What is the first step in solving the equation x² - 2x - 4 = 0 by completing the square?

• Add 4 to both sides

• Subtract 4 from both sides

• Multiply both sides by 2

• Divide both sides by 2

What are the solutions for the equation (x - 1)² = 5?

• x = 1 ± √5

• x = -1 ± √5

• x = 1 ± 5

• x = -1 ± 5