Consecutive Odd Integers and Quadratics

The video tutorial explains how to find two positive consecutive odd integers whose product is 195. It begins by introducing the concept of consecutive odd integers and setting up an algebraic equation. The tutorial then demonstrates solving the quadratic equation by factoring, using prime factorization to identify the correct factors. Finally, it concludes by verifying the solution, identifying the integers as 13 and 15.

What is the product of the two positive consecutive odd integers we are trying to find?

• 195

• 200

• 180

• 205

How do we represent the next consecutive odd integer if the first is x?

• x + 1

• x + 2

• x + 4

• x + 3

What type of equation do we get when we set up the problem algebraically?

• Linear equation

• Exponential equation

• Cubic equation

• Quadratic equation

What is the first step in solving the quadratic equation x^2 + 2x - 195 = 0?

• Multiply both sides by 2

• Add 195 to both sides

• Subtract 195 from both sides

• Factor the equation

Which pair of numbers are the factors of -195 that add up to 2?

• -15 and 13

• -5 and 39

• -13 and 15

• -10 and 20

What is the prime factorization of 195?

• 5 x 5 x 7

• 3 x 7 x 11

• 2 x 5 x 19

• 3 x 5 x 13

What is the value of x when solving x - 13 = 0?

• 15

• 13

• -13

• -15

Why is x = -15 not a valid solution for this problem?

• Because x must be positive

• Because x must be greater than 20

• Because x must be less than 10

• Because x must be even

What are the two positive consecutive odd integers that solve the problem?

• 11 and 13

• 13 and 15

• 15 and 17

• 17 and 19

What is the sum of the two integers found in the solution?

• 28

• 30

• 32

• 34