Integer Properties and Basic Algebra

The video tutorial teaches how to use factoring to solve word problems, focusing on setting up equations for consecutive integers and solving them. It includes examples like finding two consecutive even integers whose squares sum to 340 and solving equations involving the square of a number. The lesson concludes with a preview of using factoring to solve geometric problems.

What is the most challenging part of solving word problems according to the teacher?

• Setting up the problem

• Performing calculations

• Finding the correct answer

• Understanding the question

What does 'consecutive even integers' imply in the context of the problem?

• Integers that are prime

• Integers that are odd

• Integers that follow one another and are even

• Integers that are negative

If x is the first even integer, what expression represents the second consecutive even integer?

• x + 1

• x + 2

• x + 3

• x + 4

What is the equation formed by the sum of the squares of two consecutive even integers equaling 340?

• x^2 + (x + 1)^2 = 340

• x^2 + (x + 4)^2 = 340

• x^2 + (x + 2)^2 = 340

• x^2 + (x + 3)^2 = 340

What is the first step in solving the equation x^2 + 4x + 4 = 340?

• Divide both sides by 2

• Multiply both sides by 2

• Subtract 340 from both sides

• Add 340 to both sides

What two numbers multiply to 168 and add to 2 in the factoring process?

• 14 and -12

• 8 and 20

• 12 and 14

• 10 and 16

What is the value of x if the integers must be positive?

• 12

• -14

• -12

• 14

What is the second integer if the first integer is 12?

• 18

• 14

• 16

• 10

In the new problem, what does '14 less than the square of a number' translate to in an equation?

• x - 14

• x^2 + 14

• x + 14

• x^2 - 14

What is the equation formed when 14 less than the square of a number equals five times the number?

• x^2 + 14 = 5x

• x^2 - 5 = 14x

• x^2 + 5 = 14x

• x^2 - 14 = 5x