Factoring and Solving Quadratic Equations

The video tutorial explains how to find two positive consecutive even integers whose product is 728. It begins by setting up an equation using a variable to represent one integer and its consecutive counterpart. The tutorial then demonstrates solving the quadratic equation by factoring, using prime factorization to find the necessary factors. Finally, it identifies the two integers as 26 and 28, excluding negative solutions, and concludes with a complete sentence answer.

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

• 1024

• 512

• 256

• 728

How do you find the next consecutive even integer if you start with a positive even integer x?

• Subtract 2

• Multiply by 2

• Add 2

• Add 1

What is the equation formed to find the two consecutive even integers?

• x^2 - 2x = 728

• x + (x + 2) = 728

• x * (x + 2) = 728

• x^2 + 2x = 728

What type of equation is x^2 + 2x - 728 = 0?

• Cubic

• Linear

• Quadratic

• Exponential

What is the prime factorization of 728?

• 2 x 2 x 2 x 5 x 13

• 2 x 3 x 3 x 7 x 13

• 2 x 2 x 2 x 7 x 13

• 2 x 2 x 3 x 7 x 13

Which two numbers multiply to -728 and add to 2?

• -26 and 28

• -28 and 26

• -13 and 56

• -14 and 52

What are the binomial factors of the equation x^2 + 2x - 728 = 0?

• (x + 14)(x - 52)

• (x - 13)(x + 56)

• (x + 26)(x - 28)

• (x - 26)(x + 28)

What is the value of x when solving x - 26 = 0?

• -28

• 28

• -26

• 26

What is the value of x when solving x + 28 = 0?

• 28

• -26

• 26

• -28

What are the two positive consecutive even integers that multiply to 728?

• 30 and 32

• 26 and 28

• 28 and 30

• 24 and 26