DIAMOND PROBLEMS

Front

What are diamond problems in mathematics?

Back

Diamond problems are a type of problem that involves finding two numbers that multiply to a given product and add to a given sum.

Front

What is the product of the numbers in a diamond problem?

Back

The product is the result of multiplying the two numbers together.

Front

What is the sum of the numbers in a diamond problem?

Back

The sum is the result of adding the two numbers together.

Front

If the product is 12 and the sum is 8, what are the two numbers?

Back

The two numbers are 6 and 2.

Front

If the product is -12 and the sum is -4, what are the two numbers?

Back

The two numbers are -6 and 2.

Front

What does it mean if a diamond problem has no solution?

Back

It means there are no two numbers that can satisfy both the product and sum conditions.

Front

How do you factor the expression x² - 4?

Back

x² - 4 can be factored as (x + 2)(x - 2).

Front

What is the first step in solving a diamond problem?

Back

Identify the product and the sum from the problem statement.

Front

What are the possible pairs of numbers for a product of 12?

Back

The pairs are (1, 12), (2, 6), (3, 4), (-1, -12), (-2, -6), (-3, -4).

Front

If the sum of two numbers is 0, what can you conclude about their values?

Back

One number is the negative of the other.