Factors, Quadratics, and Consecutive Numbers

The video tutorial explains how to find two consecutive page numbers whose product is 342. It begins by setting up a quadratic equation, x(x + 1) = 342, and simplifies it to x^2 + x - 342 = 0. The tutorial then demonstrates factoring the equation by finding the prime factorization of 342, which is 2 * 3 * 3 * 19, leading to the factors 18 and 19. The solutions to the equation are x = 18 and x = -19, but since a page number cannot be negative, the consecutive page numbers are 18 and 19.

What is the product of the two consecutive page numbers we are trying to find?

• 340

• 341

• 342

• 343

If the first page number is X, what expression represents the next consecutive page number?

• X+2

• X+1

• X-1

• X

What is the quadratic equation derived from the problem statement?

• x^2 + x - 342 = 0

• x^2 - x - 342 = 0

• x^2 + x + 342 = 0

• x^2 - x + 342 = 0

What is the first step in solving the quadratic equation by factoring?

• Dividing both sides by x

• Multiplying both sides by 2

• Subtracting 342 from both sides

• Adding 342 to both sides

Which number is NOT a factor of 342?

• 19

• 2

• 3

• 5

What is the prime factorization of 342?

• 2 * 3 * 3 * 19

• 3 * 3 * 3 * 19

• 2 * 3 * 5 * 19

• 2 * 2 * 3 * 19

What are the two binomial factors of the quadratic equation?

• (x + 19)(x - 18)

• (x + 17)(x - 20)

• (x + 18)(x - 19)

• (x + 20)(x - 17)

What is the value of X that represents the first page number?

• 20

• 19

• 18

• 17

What is the second consecutive page number if the first is 18?

• 17

• 19

• 20

• 18

What is the final solution to the problem of finding the consecutive page numbers?

• 20 and 21

• 19 and 20

• 18 and 19

• 17 and 18