Trial and Error Method in Mathematics

Mr. D explains a system of inequalities problem involving positive integers P and Q. The problem requires factoring the expression p squared minus q squared and analyzing the inequalities p plus q greater than 4 and p minus q greater than 0. Through trial and error, Mr. D identifies possible values for the factors and solves the system of equations to find that P equals 3.

What are the given conditions for the integers p and Q in the problem?

• p and Q are negative integers

• p is less than Q

• p and Q are positive integers

• p is equal to Q

What mathematical concept is used to factor p^2 - Q^2?

• Sum of cubes

• Difference of squares

• Quadratic formula

• Binomial theorem

What is the inequality condition for P + Q?

• P + Q ≤ 4

• P + Q > 4

• P + Q = 4

• P + Q < 4

What is the inequality condition for P - Q?

• P - Q = 0

• P - Q < 0

• P - Q ≤ 0

• P - Q > 0

What is the significance of the condition P > Q?

• It ensures P is less than Q

• It ensures P is greater than Q

• It ensures P is a positive integer

• It ensures P is a negative integer

What is the first whole number greater than 4 for P + Q?

• 6

• 5

• 3

• 4

What is the smallest possible value for P - Q?

• 1

• 2

• 0

• 3

Why can't P + Q be 6 in this problem?

• Because Q must be greater than P

• Because 6 is not a whole number

• Because it does not satisfy the inequality

• Because P must be less than Q

What happens if you try P + Q = 7?

• It results in a negative product

• It is not a valid option

• It does not satisfy the inequality

• It satisfies the inequality

What is the result of multiplying 5 and 1 in the trial and error method?

• 7

• 8

• 5

• 6